1800
18002 = 803 + 1003 + 1203 = 304 + 304 + 304 + 304.
Komachi equation: 18002 = 12 / 22 * 34562 + 72 * 82 * 92.
18002 = (1)(2)(3)(4)(5)(6 + 7 + 8 + 9)(10 + 11 + 12 + 13 + 14)(15),
18002 = (1)(2)(3)(4 + 5 + 6 + ... + 12)(13 + 14 + 15 + 16 + 17)(18 + 19 + 20 + 21 + 22),
18002 = (1)(2)(3)(4 + 5 + 6 + 7 + 8)(9 + 10 + 11 + ... + 23)(24 + 25 + 26),
18002 = (1)(2)(3)(4 + 5 + 6 + 7 + 8)(9 + 10 + 11)(12 + 13 + 14 + ... + 36),
18002 = (1)(2)(3 + 4 + 5 + 6)(7 + 8 + 9 + 10 + 11)(12 + 13)(14 + 15 + 16 + 17 + 18),
18002 = (1)(2)(3 + 4 + 5 + 6 + 7)(8)(9)(10 + 11 + 12 + 13 + 14)(15),
18002 = (1)(2)(3 + 4 + 5 + 6 + 7)(8)(9 + 10 + 11 + ... + 18)(19 + 20 + 21),
18002 = (1)(2)(3 + 4 + 5 + 6 + 7)(8 + 9 + 10 + 11 + 12)(13 + 14)(15 + 16 + 17),
18002 = (1)(2)(3 + 4 + 5 + 6 + 7)(8 + 9 + 10)(11 + 12 + 13 + 14)(15 + 16 + 17),
18002 = (1)(2 + 3)(4)(5)(6)(7 + 8)(9 + 10 + 11)(12),
18002 = (1)(2 + 3)(4)(5)(6 + 7 + 8 + ... + 14)(15 + 16 + 17 + ... + 30),
18002 = (1)(2 + 3)(4)(5 + 6 + 7 + ... + 10)(11 + 12 + 13 + ... + 85),
18002 = (1)(2 + 3)(4 + 5)(6)(7 + 8 + 9)(10)(11 + 12 + 13 + 14),
18002 = (1)(2 + 3 + 4 + 5 + 6)(7 + 8)(9)(10 + 11 + 12 + ... + 15)(16),
18002 = (1)(2 + 3 + 4 + 5 + 6)(7 + 8 + 9 + 10 + 11)(12)(13 + 14 + 15 + ... + 27),
18002 = (1)(2 + 3 + 4 + 5 + 6)(7 + 8 + 9 + 33)(34 + 35 + 36 + ... + 41),
18002 = (1)(2 + 3 + 4 + 5 + 6)(7 + 8 + 9)(10 + 11 + 12 + ... + 15)(16 + 17 + 18 + ... + 20),
18002 = (1)(2 + 3 + 4)(5)(6)(7 + 8 + 9)(10)(11 + 12 + 13 + 14),
18002 = (1 + 2)(3 + 4 + 5 + ... + 17)(18 + 19 + 20 + 21 + 22)(23 + 24 + 25),
18002 = (1 + 2)(3 + 4 + 5 + 6 + 7)(8)(9 + 10 + 11 + ... + 16)(17 + 18 + 19),
18002 = (1 + 2 + 3 + 4)(5)(6 + 7 + 8 + 9 + 10)(11 + 12 + 13)(14 + 15 + 16),
18002 = (1 + 2 + 3 + 4)(5 + 6 + 7 + ... + 19)(20)(21 + 22 + 23 + 24),
18002 = (1 + 2 + 3 + 4)(5 + 6 + 7 + ... + 20)(21 + 22 + 23 + ... + 60),
18002 = (1 + 2 + 3)(4)(5)(6 + 7 + 8 + 9)(10 + 11 + 12 + 13 + 14)(15),
18002 = (1 + 2 + 3)(4 + 5 + 6 + ... + 12)(13 + 14 + 15 + 16 + ... + 17)(18 + 19 + 20 + 21 + 22),
18002 = (1 + 2 + 3)(4 + 5 + 6 + 7 + 8)(9 + 10 + 11 + ... + 23)(24 + 25 + 26),
18002 = (1 + 2 + 3)(4 + 5 + 6 + 7 + 8)(9 + 10 + 11)(12 + 13 + 14 + ... + 36).
by Yoshio Mimura, Kobe, Japan
1801
18012 = 3243601, a zigzag square.
18012 = 66 + 66 + 66 + 76 + 126.
Page of Squares : First Upload February 26, 2007 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1803
18032 = 3250809, a zigzag square.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1804
A cubic polynomial :
(X + 18042)(X + 21122)(X + 25832) = X3 + 37932X2 + 81234122X + 98413539842.
by Yoshio Mimura, Kobe, Japan
1805
18052 = (48 + 49 + 50 + ... + 66)2 + (67 + 68 + 69 + ... + 85)2 + (86 + 87 + 88 + ... + 104)2 + ... + (67 + 68 + 69 + ... + 85)2.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1806
18062 = 3261636, a zigzag square.
18062± 5 are primes.
18062 = (32 + 5)(92 + 5)(522 + 5).
18062 = 193 + 1053 + 1283.
(18062 - 6) = (32 - 6)(82 - 6)(112 - 6)(132 - 6).
Page of Squares : First Upload February 26, 2007 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1807
404768k + 722800k + 851097k + 1286584k are squares for k = 1,2,3 (18072, 17509832, 17860912032).
Page of Squares : First Upload May 10, 2011 ; Last Revised May 10, 2011by Yoshio Mimura, Kobe, Japan
1808
18082 = 683 + 763 + 1363.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1809
18092 = 3272481, 3 * 2 * 72 * 4 + 81 = 1809.
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
1809 - 405 - 41 - ... - 5072 - 7684 - 12832 - 1809
(Note f(1809) = 182 + 092 = 405, f(405) = 42 + 052 = 41, etc. See 41)
by Yoshio Mimura, Kobe, Japan
1810
18102 = 15 + 35 + 75 + 95 + 205.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1812
18122± 5 are primes.
18122 = 363 + 943 + 1343.
18125 = 19533990254072832 : 192 + 52 + 332 + 92 + 92 + 02 + 22 + 52 + 42 + 02 + 72 + 22 + 82 + 32 + 22 = 1812.
226k + 610k + 822k + 1478k are squares for k = 1,2,3 (562, 18122, 634242).
Page of Squares : First Upload July 14, 2008 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1813
18132 = 3286969, a zigzag square.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1814
12 + 22 + 32 + 42 + ... + 18142 = 1991359315, the first 10-digit sum consisting of odd digits (there are such 4 sums in all, cf. 2526, 2773, 3014).
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1815
18152 = (1)(2 + 3)(4 + 5)(6 + 7 + 8 + ... + 16)(17 + 18 + 19 + ... + 38),
18152 = (1)(2 + 3 + 4)(5)(6 + 7 + 8 + ... + 16)(17 + 18 + 19 + ... + 38).
by Yoshio Mimura, Kobe, Japan
1816
18162 = 3297856, a zigzag square with different digits.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1817
18172 = 503 + 1123 + 1213 = 64 + 174 + 184 + 424.
A cubic polynomial :
(X + 4682)(X + 11042)(X + 18172) = X3 + 21772X2 + 22391882X + 9387930242.
by Yoshio Mimura, Kobe, Japan
1818
18182 = 3305124, 32 + 32 + 02 + 52 + 12 + 22 + 42 = 82.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1819
S2(1819) = S2(77) + S2(211), where S2(n) = 12 + 22 + 32 + ... + n2.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1821
18212 = 253 + 683 + 1443.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1822
18222 + 18232 + 18242 + ... + 74892 = 74902 + 74912 + 74922 + ... + 94132.
Page of Squares : First Upload September 9, 2011 ; Last Revised September 9, 2011by Yoshio Mimura, Kobe, Japan
1823
18232 = 3323329, a square with just 3 kinds of digits.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1824
18242 = 443 + 1483.
18242 = 483 + 205 + 47.
Komachi equations:
18242 = 92 * 82 * 762 * 52 * 42 / 32 / 22 / 102 = 92 * 82 * 762 / 52 / 42 / 32 * 22 * 102.
by Yoshio Mimura, Kobe, Japan
1826
1 / 1826 = 0.0005476...., 5476 = 742.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1827
18272± 2 are primes.
Page of Squares : First Upload December 29, 2013 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan
1828
18282 = 1372 + 1382 + 1392 + 1402 + 1412 + 1422 + ... + 2322.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1830
18302 = 13 + 23 + 33 + 43 + 53 + 63 + ... + 603.
18302 + 18312 + 18322 + ... + 18602 = 18612 + 18622 + 18632 + ... + 18902.
990k + 1020k + 1785k + 1830k are squares for k = 1,2,3 (752, 29252, 1176752).
Page of Squares : First Upload February 26, 2007 ; Last Revised September 9, 2011by Yoshio Mimura, Kobe, Japan
1832
18322 = 3356224, 33 * 56 - 2 * 2 * 4 = 1832.
18322 = 1632 + 1652 + 1672 + 1692 + 1702 + 1712 + ... +2892.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1833
S2(1833) = S2(148) + S2(189), where S2(n) = 12 + 22 + 32 + ... + n2.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1834
18342 = 3363556, a square with just 3 kinds of digits.
18342 = 3363556, 3 * 3 * 6 * 35 - 56 = 1834.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1836
18362 = 243 + 903 + 1383.
18362 = (12 + 8)(32 + 8)(102 + 8)(142 + 8) = (22 + 8)(142 + 8)(372 + 8) = (22 + 8)(5302 + 8).
A cubic polynomial :
(X + 9122)(X + 12112)(X + 18362) = X3 + 23812X2 + 29944922X + 20277371522.
18362 = (1)(2)(3 + 4 + 5)(6 + 7 + 8 + 9 + 10 + 11)(12 + 13 + 14 + 15)(16 + 17 + 18),
18362 = (1 + 2)(3)(4)(5 + 6 + 7)(8 + 9)(10 + 11 + 12 + ... + 26),
18362 = (1 + 2)(3 + 4 + 5 + 6)(7 + 8 + 9 + 10)(11 + 12 + 13 + ... + 61),
18362 = (1 + 2)(3 + 4 + 5)(6 + 7 + 8 + 9 + 10 + 11)(12)(13 + 14 + 15 + ... + 21).
by Yoshio Mimura, Kobe, Japan
1837
18372 = 3374569, 32 + 32 + 72 + 42 + 52 + 62 + 92 = 152.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1838
18382 = 3378244, 33 * 7 * 8 - 2 - 4 - 4 = 1838.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1839
18392± 2 are primes.
18392 = 3381921, 32 + 32 + 82 + 12 + 92 + 22 + 12 = 132.
Page of Squares : First Upload February 26, 2007 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan
1840
18402 = 443 + 683 + 1443.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1841
Komachi equation: 18412 = 12 / 22 / 32 / 42 * 562 * 7892.
Page of Squares : First Upload September 7, 2010 ; Last Revised September 7, 2010by Yoshio Mimura, Kobe, Japan
1843
18434 = 11537224429201, and 12 + 12 + 52 + 32 + 72 + 222 + 42 + 42 + 292 + 202 + 12 = 1843.
Page of Squares : First Upload December 1, 2008 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
1844
18442 = 643 + 983 + 1303.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1845
18455 = 21378727540153125 : 22 + 12 + 372 + 82 + 72 + 22 + 72 + 52 + 42 + 02 + 152 + 32 + 12 + 22 + 52 = 1845.
Komachi equations:
18452 = 16 * 26 + 36 * 46 - 56 + 66 + 76 - 86 + 96 = 96 - 86 + 76 + 66 - 56 + 46 * 36 + 26 */ 16.
by Yoshio Mimura, Kobe, Japan
1847
18472 = 44 + 184 + 214 + 424.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1848
18482 = 493 + 723 + 1433.
18482 = (1)(2)(3 + 4 + 5 + ... + 13)(14 + 15 + 16 + ... + 35)(36),
18482 = (1)(2)(3 + 4 + 5 + ... + 8)(9 + 10 + 11 + ... + 24)(25 + 26 + 27 + ... + 31),
18482 = (1)(2)(3 + 4 + 5)(6 + 7 + 8 + ... + 533),
18482 = (1)(2 + 3 + 4 + ... + 12)(13 + 14 + 15)(16 + 17 + 18 + ... + 48),
18482 = (1)(2 + 3 + 4 + 5)(6 + 7 + 8 + ... + 698),
18482 = (1 + 2)(3)(4)(5 + 6)(7)(8)(9 + 10 + 11 + ... + 19),
18482 = (1 + 2)(3 + 4)(5 + 6)(7)(8)(9 + 10 + 11 + ... + 24).
by Yoshio Mimura, Kobe, Japan
1849
The square of 43.
18492 = 863 + 863 + 1293.
A cubic polynomial :
(X + 5042)(X + 9992)(X + 14722) = X3 + 18492X2 + 17223122 + 7411461122.
by Yoshio Mimura, Kobe, Japan
1850
18502 = (12 + 1)(32 + 1)(62 + 1)(682 + 1) = (22 + 1)(32 + 1)(62 + 1)(432 + 1)
= (22 + 1)(72 + 1)(1172 + 1) = (62 + 1)(72 + 1)(432 + 1).
by Yoshio Mimura, Kobe, Japan
1851
18512 = 3426201, 342 * 6 - 201 = 1851.
18512 = 93 + 883 + 1403 = 643 + 843 + 1373.
Page of Squares : First Upload February 26, 2007 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1852
126k + 538k + 1050k + 1422k are squares for k = 1,2,3 (562, 18522, 647362).
Page of Squares : First Upload May 10, 2011 ; Last Revised May 10, 2011by Yoshio Mimura, Kobe, Japan
1856
18562 = (12 + 7)(152 + 7)(432 + 7).
Page of Squares : First Upload May 10, 2011 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1858
18582 = 74 + 74 + 134 + 434.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1859
The square root of 1859 is 43.11612..., and 43 = 12 + 12 + 62 + 12 + 22.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1862
Komachi equation: 18622 = 982 * 762 / 52 * 42 / 322 * 102.
Page of Squares : First Upload September 7, 2010 ; Last Revised September 7, 2010by Yoshio Mimura, Kobe, Japan
1863
18632 = 94 + 124 + 244 + 424 = 94 + 184 + 364 + 364 = 124 + 134 + 344 + 384.
A cubic polynomial :
(X + 5602)(X + 18632)(X + 42842) = X3 + 47052X2 + 83989082X + 44694115202.
The second square which is the sums of four 4th powers in 3 ways :
18632 = 94 + 124 + 244 + 424 = 94 + 184 + 364 + 364 = 124 + 134 + 344 + 384.
by Yoshio Mimura, Kobe, Japan
1865
18652 = 3478225, 3 * 4 * 78 * 2 - 2 - 5 = 1865.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1866
18662 = 3481956, a square with different digits.
18662 = S2(99) + S2(211), where S2(n) = 12 + 22 + 32 + ... + n2.
464634k + 696018k + 1065486k + 1255818k are squares for k = 1,2,3 (18662, 18473402, 19046299322).
Page of Squares : First Upload February 26, 2007 ; Last Revised May 10, 2011by Yoshio Mimura, Kobe, Japan
1867
18672 = 3485689, 3 + 4 * 8 * 56 + 8 * 9 = 1867.
18672 = 203 + 1103 + 1293.
Page of Squares : First Upload February 26, 2007 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1869
18692 = 83 + 493 + 1503.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1870
18702 = (1 + 2 + 3 + 4)(5 + 6)(7 + 8 + 9 + 10)(11 + 12 + 13 + ... + 44).
704k + 1034k + 1870k + 6193k are squares for k = 1,2,3 (992, 65892, 4954952).
Page of Squares : First Upload February 26, 2007 ; Last Revised May 10, 2011by Yoshio Mimura, Kobe, Japan
1872
18722 = 3504384, a zigzag square.
Komachi equation: 18722 = 92 * 82 * 72 * 652 * 42 * 32 / 2102.
18722 = (1)(2)(3)(4 + 5 + 6 + ... + 9)(10 + 11 + 12 + ... + 22)(23 + 24 + 25),
18722 = (1)(2 + 3 + 4 + ... + 14)(15 + 16 + 17)(18)(19 + 20),
18722 = (1 + 2 + 3)(4 + 5 + 6 + ... + 9)(10 + 11 + 12 + ... + 22)(23 + 24 + 25).
by Yoshio Mimura, Kobe, Japan
1873
18732 = 3508129, a square with different digits.
18732 = 573 + 993 + 1333.
Page of Squares : First Upload February 26, 2007 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1874
1 / 1874 = 0.00053361..., and 53361 = 2312.
18742 = 3511876, 3 - 5 + 1 * 1876 = 3 - 5 * 1 + 1876 = 1874.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1875
18752 = 3515625, 3 * 5 * 1 / 5 * 625 = 3 / 5 * 1 * 5 * 625 = 1875.
18752 = 253 + 503 + 1503.
18752 = (1 + 2)(3 + 4 + 5 + 6 + 7)(8 + 9 + 10 + ... + 17)(18 + 19 + 20 + ... + 32).
Page of Squares : First Upload February 26, 2007 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1876
18762 = 3519376, a zigzag square with odd digits except the last digit 6.
Page of Squares : First Upload February 26, 2007 ; Last Revised August 24, 2013by Yoshio Mimura, Kobe, Japan
1877
18772 = 593 + 953 + 1353.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1878
The square root of 1878 is 43.335..., and 43 = 32 + 32 + 52.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1880
18802= 145 x 146 + 146 x 147 + 147 x 148 + 148 x 149 + 149 x 150 + ...+ 238 x 239.
18802 = 713 + 1123 + 1213.
The sum of the squares of divisors of 1880 is a square, 22102.
Komachi equation: 18802 = 9872 * 62 * 52 * 42 / 32 / 212.
Page of Squares : First Upload February 26, 2007 ; Last Revised November 1, 2011by Yoshio Mimura, Kobe, Japan
1881
18812 = 3538161, a zigzag square.
18812 = (12 + 2)(32 + 2)(132 + 2)(252 + 2) = (12 + 2)(32 + 2)(52 + 2)(632 + 2) = (12 + 8)(72 + 8)(832 + 8).
Page of Squares : First Upload February 26, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1883
18832 = 3545689, 32 + 52 + 42 + 52 + 62 + 82 + 92 = 162.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1884
18842 = 3549456, 3 + 5 * 4 * 94 - 5 + 6 = 3 - 5 + 4 * 94 * 5 + 6 = 1884.
18842 = 223 + 303 + 1523.
66k + 210k + 1230k + 1410k are squares for k = 1,2,3 (542, 18842, 683642).
Page of Squares : First Upload February 26, 2007 ; Last Revised May 10, 2011by Yoshio Mimura, Kobe, Japan
1885
18852 = 3553225, a square with just 3 kinds of digits.
18852 = (22 + 1)(122 + 1)(702 + 1).
18852 = S2(137) + S2(200), where S2(n) = 12 + 22 + 32 + ... + n2.
Page of Squares : First Upload February 26, 2007 ; Last Revised November 2, 2013by Yoshio Mimura, Kobe, Japan
1887
1 / 1887 = 0.000529...., and 529 = 232.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1888
1 / 1888 = 0.000529...., and 529 = 232.
The square root of 1888 is 43.4511..., and 43 = 42 + 52 + 12 + 12.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1889
1 / 1889 = 0.000529...., and 529 = 232.
18892 = 43 + 893 + 1423.
Page of Squares : First Upload February 26, 2007 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1890
Komachi equations:
18902 = 92 * 82 * 72 * 62 * 52 * 42 / 322 */ 12 = 92 / 82 * 72 * 62 * 52 / 42 * 322 */ 12
= 982 / 72 / 62 * 542 * 32 / 22 * 102.
18902 = (12 + 5)(22 + 5)(102 + 5)(252 + 5) = (12 + 5)(22 + 5)(42 + 5)(52 + 5)(102 + 5)
= (12 + 5)(32 + 5)(102 + 5)(202 + 5) = (22 + 5)(42 + 5)(52 + 5)(252 + 5)
= (22 + 5)(52 + 5)(102 + 5)(112 + 5) = (22 + 5)(52 + 5)(1152 + 5) = (32 + 5)(202 + 5)(252 + 5)
= (32 + 5)(42 + 5)(52 + 5)(202 + 5) = (42 + 5)(52 + 5)(72 + 5)(102 + 5) = (52 + 5)(172 + 5)(202 + 5)
= (72 + 5)(102 + 5)(252 + 5).
18902 = (1)(2)(3)(4 + 5)(6 + 7 + 8 + ... + 12)(13 + 14 + 15 + ... + 47),
18902 = (1)(2)(3)(4 + 5)(6 + 7 + 8 + 9)(10 + 11)(12 + 13 + 14 + ... + 18),
18902 = (1)(2)(3)(4 + 5)(6 + 7 + 8)(9 + 10 + 11 + 12)(13 + 14 + 15 + 16 + 17),
18902 = (1)(2)(3)(4 + 5)(6 + 7 + 8)(9 + 10 + 11)(12 + 13 + 14 + 15 + 16 + 17 + 18),
18902 = (1)(2)(3)(4 + 5 + 6 + ... + 24)(25)(26 + 27 + 28),
18902 = (1)(2)(3)(4 + 5 + 6 + ... + 31)(32 + 33 + 34 + ... + 58),
18902 = (1)(2)(3)(4 + 5 + 6 + 7 + 8)(9)(10 + 11)(12 + 13 + 14 + ... + 18),
18902 = (1)(2)(3 + 4 + 5 + ... + 11)(12 + 13)(14 + 15 + 15 + ... + 49),
18902 = (1)(2)(3 + 4 + 5 + 6)(7 + 8)(9)(10 + 11 + 12 + ... + 39),
18902 = (1)(2)(3 + 4 + 5 + 6 + 7)(8 + 9 + 10 + ... + 13)(14 + 15 + 15 + ... + 49),
18902 = (1)(2)(3 + 4 + 5 + 6 + 7)(8 + 9 + 10 + ... + 28)(29 + 30 + 31 + ... + 34),
18902 = (1)(2)(3 + 4 + 5 + 6 + 7)(8 + 9 + 10)(11 + 12 + 13 + ... + 73),
18902 = (1)(2)(3 + 4 + 5 + ... + 9)(10 + 11 + 12 + ... + 44)(45),
18902 = (1)(2 + 3)(4 + 5)(6 + 7 + 8)(9)(10 + 11 + 12 + ... + 30),
18902 = (1)(2 + 3)(4 + 5 + 6 + ... + 10)(11 + 12 + 13)(14 + 15 + 16 + ... + 31),
18902 = (1)(2 + 3 + 4 + ... + 16)(17 + 18 + 19 + ... + 23)(24 + 25 + 26 + ... + 30),
18902 = (1)(2 + 3 + 4 + ... + 16)(17 + 18 + ... + 25)(26 + 27 + 28 + 29 + 30),
18902 = (1)(2 + 3 + 4 + ... + 19)(20)(21)(22 + 23),
18902 = (1)(2 + 3 + 4 + ... + 19)(20 + 21 + 22 + ... + 25)(26 + 27 + 28 + 29 + 30),
18902 = (1)(2 + 3 + 4 + 5)(6)(7 + 8 + 9 + ... + 20)(21 + 22 + 23 + ... + 29),
18902 = (1)(2 + 3 + 4 + 5)(6 + 7 + 8)(9)(10)(11 + 12 + 13 + ... + 19),
18902 = (1)(2 + 3 + 4 + 5 + 6)(7)(8 + 9 + 10 + ... + 13)(14 + 15 + 16 + ... + 31),
18902 = (1)(2 + 3 + 4 + 5 + 6)(7 + 8 + 9 + ... + 20)(21)(22 + 23),
18902 = (1)(2 + 3 + 4)(5)(6 + 7 + 8)(9)(10 + 11 + 12 + ... + 30),
18902 = (1)(2 + 3 + 4)(5 + 6 + 7)(8 + 9 + 10 + ... + 22)(23 + 24 + 25 + ... + 26),
18902 = (1 + 2)(3)(4)(5 + 6 + 7 + ... + 445),
18902 = (1 + 2)(3)(4 + 5)(6 + 7 + 8 + ... + 14)(15 + 16 + 17 + ... + 34),
18902 = (1 + 2)(3)(4 + 5)(6 + 7 + 8 + 9)(10 + 11)(12 + 13 + 14 + 15 + 16),
18902 = (1 + 2)(3)(4 + 5)(6 + 7 + 8)(9 + 10 + 11)(12 + 13 + 14 + 15 + 16),
18902 = (1 + 2)(3)(4 + 5 + 6 + 7 + 8)(9)(10 + 11)(12 + 13 + 14 + 15 + 16),
18902 = (1 + 2)(3)(4 + 5 + 6)(7)(8 + 9 + 10 + ... + 16)(17 + 18),
18902 = (1 + 2)(3)(4 + 5 + 6)(7 + 8)(9 + 10 + 11 + 12)(13 + 14 + 15),
18902 = (1 + 2)(3 + 4)(5)(6 + 7 + 8 + 9)(10 + 11)(12 + 13 + 14 + 15),
18902 = (1 + 2)(3 + 4)(5)(6 + 7 + 8)(9 + 10 + 11)(12 + 13 + 14 + 15),
18902 = (1 + 2)(3 + 4 + 5 + ... + 11)(12)(13 + 14 + 15 + ... + 57),
18902 = (1 + 2)(3 + 4 + 5 + ... + 11)(12 + 13 + 14 + 15 + 16)(17 + 18 + 19 + ... + 28),
18902 = (1 + 2)(3 + 4 + 5 + ... + 11)(12 + 13 + 14 + ... + 18)(19 + 20 + 21 + ... + 26),
18902 = (1 + 2)(3 + 4 + 5 + 6 + 7)(8 + 9 + 10)(11 + 12 + 13 + ... + 17)(18),
18902 = (1 + 2)(3 + 4 + 5 + ... + 9)(10)(11 + 12 + 13 + ... + 16)(17 + 18),
18902 = (1 + 2)(3 + 4 + 5)(6 + 7 + 8 + ... + 12)(13 + 14 + 15 + ... + 57),
18902 = (1 + 2)(3 + 4 + 5)(6 + 7 + 8)(9)(10 + 11)(12 + 13),
18902 = (1 + 2 + 3 + 4)(5 + 6 + 7)(8 + 9 + 10 + ... + 13)(14 + 15 + 16 + ... + 28),
18902 = (1 + 2 + 3 + 4)(5 + 6 + 7)(8 + 9 + 10 + ... + 34)(35),
18902 = (1 + 2 + 3 + 4 + 5)(6 + 7 + 8 + ... + 12)(13 + 14 + 15)(16 + 17 + 18 + 19 + 20),
18902 = (1 + 2 + 3 + ... + 6)(7 + 8 + 9 + 10 + 11)(12 + 13 + 14 + 15)(16 + 17 + 18 + 19),
18902 = (1 + 2 + 3 + ... + 6)(7 + 8 + 9 + 10 + 11)(12 + 13 + 14 + 15 + 16)(17 + 18 + 19),
18902 = (1 + 2 + 3 + ... + 6)(7 + 8 + 9 + ... + 13)(14 + 15 + 16)(17 + 18 + 19),
18902 = (1 + 2 + 3 + ... + 7)(8 + 9 + 10 + ... + 22)(23 + 24 + 25 + ... + 40),
18902 = (1 + 2 + 3 + ... + 7)(8 + 9 + 10 + ... + 34)(35 + 36 + 37 + ... + 40),
18902 = (1 + 2 + 3 + ... + 8)(9 + 10 + 11 + ... + 26)(27 + 28 + 29 + ... + 36),
18902 = (1 + 2 + 3 + ... + 9)(10 + 11)(12 + 13 + 14 + 15)(16 + 17 + 18 + 19),
18902 = (1 + 2 + 3 + ... + 9)(10 + 11)(12 + 13 + 14 + 15 + 16)(17 + 18 + 19),
18902 = (1 + 2 + 3)(4 + 5)(6 + 7 + 8 + ... + 12)(13 + 14 + 15 + ... + 47),
18902 = (1 + 2 + 3)(4 + 5)(6 + 7 + 8 + 9)(10 + 11)(12 + 13 + 14 + ... + 18),
18902 = (1 + 2 + 3)(4 + 5)(6 + 7 + 8)(9 + 10 + 11 + 12)(13 + 14 + 15 + 16 + 17),
18902 = (1 + 2 + 3)(4 + 5)(6 + 7 + 8)(9 + 10 + 11)(12 + 13 + 14 + ... + 18),
18902 = (1 + 2 + 3)(4 + 5 + 6 + ... + 24)(25)(26 + 27 + 28),
18902 = (1 + 2 + 3)(4 + 5 + 6 + ... + 31)(32 + 33 + 34 + ... + 58),
18902 = (1 + 2 + 3)(4 + 5 + 6 + 7 + 8)(9)(10 + 11)(12 + 13 + 14 + ... + 18).
by Yoshio Mimura, Kobe, Japan
1891
1891 = (12 + 22 + 32 + ... + 302) / (12 + 22).
18912 = 13 + 23 + 33 + 43 + 53 + 63 + ... + 613.
Page of Squares : First Upload February 26, 2007 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
1893
18932 = 3583449, 3 * 583 + 4 * 4 * 9 = 1893.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1894
18942 = 3587236, 32 + 52 + 82 + 72 + 22 + 32 + 62 = 142.
Page of Squares : First Upload February 26, 2007 ; Last Revised February 26, 2007by Yoshio Mimura, Kobe, Japan
1895
18952 = 85 + 125 + 175 + 185.
Page of Squares : First Upload July 14, 2008 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1896
18962 = 3594816, a square with different digits.
1 / 1896 = 0.00052742616033, 52 + 22 + 72 + 42 + 262 + 12 + 62 + 0332 = 1896.
18962 = 3594816, 3 * 5 * 94 + 81 * 6 = 3 + 59 * 4 * 8 - 1 + 6 = 1896.
18962 = 833 + 1093 + 1203.
Page of Squares : First Upload February 26, 2007 ; Last Revised July 14, 2008by Yoshio Mimura, Kobe, Japan
1898
18982 = 3602404, 32 + 62 + 02 + 22 + 42 + 02 + 42 = 92.
18982 = 3602404, and 324 = 182, 64 = 82, 00 = 02.
18982 = 95 + 95 + 125 + 155 + 195.
1898k + 4862k + 5954k + 20410k are squares for k = 1,2,3 (1822, 218922, 29723722).
Page of Squares : First Upload February 26, 2007 ; Last Revised May 10, 2011by Yoshio Mimura, Kobe, Japan