2900
29002 = (12 + 1)(22 + 1)(32 + 1)(72 + 1)(412 + 1).
Page of Squares : First Upload November 2, 2013 ; Last Revised November 2, 2013by Yoshio Mimura, Kobe, Japan
2904
29042 = 583 + 1343 + 1803 = 883 + 1323 + 1763.
552 + 2904 = 772, 552 - 2904 = 112.
Page of Squares : First Upload July 28, 2008 ; Last Revised July 27, 2011by Yoshio Mimura, Kobe, Japan
2905
29052 = 8439025, a square with different digits.
The quadratic polynomial 2905X2 - 12600X + 20304 takes the values 1032, 822, 932, 1282, 1732, 2222 at X = 1, 2,..., 6,
Page of Squares : First Upload May 21, 2007 ; Last Revised December 15, 2008by Yoshio Mimura, Kobe, Japan
2906
29062 = 1153 + 1283 + 1693.
29062 = 8444836, and 8 - 4 + 4 + 483 * 6 = 8 + 4 - 4 + 483 * 6 = 8 / 4 * 4 + 483 * 6
= 8 * 4 / 4 + 483 * 6 = 8 + 4 / 4 * 483 * 6 = 2906.
by Yoshio Mimura, Kobe, Japan
2907
29072 = 8450649, a zigzag square.
29072 = (12 + 8)(32 + 8)(2352 + 8) = (12 + 8)(32 + 8)(72 + 8)(312 + 8).
Page of Squares : First Upload May 21, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2908
29082 = 633 + 1213 + 1863.
29082 = 2482 + 2492 + 2502 + 2512 + 2522 + 2532 + 2542 + ... + 3432.
Page of Squares : First Upload May 21, 2007 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2911
29112=8473921, a square with different digits.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2912
29122± 3 are primes.
Komachi equation: 29122 = 12 / 22 * 32 * 42 * 562 * 782 / 92.
Page of Squares : First Upload September 28, 2010 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
2913
29132 = 164 + 214 + 444 + 464.
Page of Squares : First Upload July 28, 2008 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2914
29142 = 8491396, and 8 * 4 * 91 + 3 / 9 * 6 = 8 / 4 + 91 / 3 * 96 = 2914.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2915
29155 = 210471257322321875 : 212 + 02 + 42 + 72 + 122 + 52 + 72 + 322 + 22 + 322 + 12 + 82 + 72 + 52 = 2915.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
2916
The square of 54.
29162 = 1623 + 1623 = 143 + 223 + 2043.
4-cycle : 29162=08503056 - 50302=25300900 - 30092=09054081 - 05402=00291600,
(Other examples : 1600-5600-3600-9600-1600, 2100-4100-8100-6100-2100.)
Komachi equations:
29162 = 14 / 24 * 34 * 44 * 564 / 74 / 84 * 94 = 14 / 24 * 34 * 44 / 564 * 74 * 84 * 94
= 94 * 84 * 74 * 64 * 54 / 44 * 34 / 2104 = 94 * 84 / 74 / 64 / 54 / 44 * 34 * 2104
= 94 / 84 / 74 * 64 / 54 * 44 / 34 * 2104.
by Yoshio Mimura, Kobe, Japan
2920
29202 = (22 + 4)(192 + 4)(542 + 4).
29202 = 8526400 appears in the decimal expressions of π:
π = 3.14159•••8526400••• (from the 33200th digit)
(8526400 is the ninth 7-digit square in the expression of π.)
by Yoshio Mimura, Kobe, Japan
2923
Komachi equation: 29232 = 13 - 233 + 43 + 53 * 63 * 73 - 893.
Page of Squares : First Upload September 28, 2010 ; Last Revised September 28, 2010by Yoshio Mimura, Kobe, Japan
2924
29242 = 8549776, 8 + 54 * 9 * 7 / 7 * 6 = 8 + 54 * 9 / 7 * 7 * 6 = 2924.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2925
29252 = 303 + 1303 + 1853.
29252 = (22 + 9)(42 + 9)(62 + 9)(242 + 9).
990k + 1020k + 1785k + 1830k are squares for k = 1,2,3 (752, 29252, 1176752).
Komachi equatio: 29252 = 92 / 82 / 72 * 652 * 42 / 32 * 2102.
Page of Squares : First Upload July 28, 2008 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2926
29262 + 29272 + 29282 + ... + 29642 = 29652 + 29662 + 29672 + ... + 30022.
Page of Squares : First Upload September 13, 2011 ; Last Revised September 13, 2011by Yoshio Mimura, Kobe, Japan
2927
29272 = 8567329, a square with different digits.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2928
1 / 2928 = 0.00034153005464...., 32 + 42 + 12 + 532 + 0052 + 42 + 62 + 42 = 2928.
29285 = 215206488852922368 : 22 + 152 + 22 + 02 + 62 + 482 + 82 + 82 + 52 + 22 + 92 + 22 + 22 + 32 + 62 + 82 = 2928.
Page of Squares : First Upload May 21, 2007 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
2929
29292 = 8579041, a square with different digits.
The square root of 2929 is 54.120236...., and 54 = 12 + 22 + 02 + 22 + 32 + 62.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2930
29302 = (55 + 56 + 57 + 58 + 59)2 + (60 + 61 + 62 + 63 + 64)2 + (65 + 66 + 67 + 68 + 69)2 + ... + (170 + 171 + 172 + 173 + 174)2.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2931
29312 = 8590761, a square with different digits.
29312 = 8590761, 82 + 52 + 92 + 02 + 72 + 62 + 12 = 162.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2934
29342 = 8608356, 86 + 0 + 8 * 356 = 2934.
29344 = 74103793022736, and 72 + 42 + 12 + 02 + 32 + 72 + 92 + 302 + 222 + 72 + 362 = 2934.
Page of Squares : First Upload May 21, 2007 ; Last Revised December 1, 2008by Yoshio Mimura, Kobe, Japan
2937
29372 = 143 + 1563 + 1693.
Page of Squares : First Upload July 28, 2008 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2938
29382 = 803 + 893 + 1953.
Page of Squares : First Upload July 28, 2008 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2940
29402 = 1183 + 1193 + 1203 + 1213 + 1223.
Komachi equation: 29402 = 982 / 72 / 62 * 52 * 42 * 32 * 212.
Page of Squares : First Upload November 25, 2008 ; Last Revised September 28, 2010by Yoshio Mimura, Kobe, Japan
2941
1 / 2941 = 0.0003400204012240734...., and
342 + 00202 + 42 + 0122 + 22 + 42 + 072 + 342 = 2941.
by Yoshio Mimura, Kobe, Japan
2942
29425 = 220400889011083232 : 222 + 02 + 42 + 02 + 02 + 82 + 82 + 92 + 02 + 112 + 02 + 82 + 322 + 322 = 2942.
29422 = 8655364 appears in the decimal expressions of e:
e = 2.71828•••8655364••• (from the 32758th digit)
(8655364 is the ninth 7-digit square in the expression of e.)
by Yoshio Mimura, Kobe, Japan
2943
29432 = 8661249, 8 * 6 * 61 + 2 + 4 + 9 = 8 * 6 * 61 + 24 - 9 = 2943.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2944
29442 = 843 + 1443 + 1723.
29442 = (12 + 7)(42 + 7)(112 + 7)(192 + 7) = (32 + 7)(112 + 7)(652 + 7)
= (32 + 7)(42 + 7)(52 + 7)(272 + 7) = (52 + 7)(192 + 7)(272 + 7).
by Yoshio Mimura, Kobe, Japan
2945
29452 = 8673025, a square with different digits.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2947
29472 = 8684809, a zigzag square.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2948
29482 = 8690704, a zigzag square.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2949
29492 = 403 + 803 + 2013.
29492 = 8696601 appears in the decimal expressions of e:
e = 2.71828•••8696601••• (from the 68692nd digit)
by Yoshio Mimura, Kobe, Japan
2950
29502± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
2952
29522 = 543 + 683 + 2023 = 64 + 184 + 184 + 544.
29522 = 8714304, 8 + 7 * 14 * 30 + 4 = 2952.
Page of Squares : First Upload May 21, 2007 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2954
29542 = 1110 x 1111 + 1112 x 1113 + 1114 x 1115 + 1116 x 1117 + ... + 1122 x 1123.
29545 = 224932626715877024 : 222 + 42 + 92 + 32 + 262 + 262 + 72 + 152 + 82 + 72 + 72 + 02 + 242 = 22 + 22 + 492 + 32 + 22 + 62 + 22 + 62 + 72 + 152 + 82 + 72 + 72 + 02 + 22 + 42 = 2954.
Page of Squares : First Upload May 21, 2007 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
2955
29552± 2 are primes.
29552 = 813 + 1463 + 1723.
Page of Squares : First Upload July 28, 2008 ; Last Revised December 29, 2013by Yoshio Mimura, Kobe, Japan
2956
29562 = 413 + 1113 + 1943.
29562 = 8737936, 8 + 737 / 9 * 36 = 2956.
Page of Squares : First Upload May 21, 2007 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2958
2958k + 7134k + 24708k + 33321k are squares for k = 1,2,3 (2612, 421952, 72435332).
Page of Squares : First Upload May 27, 2011 ; Last Revised May 27, 2011by Yoshio Mimura, Kobe, Japan
2960
Loop of length 56 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
2960 - 4441 - 3617 - 1585 - ... - 5650 - 5636 - 4432 - 2960
(Note f(2960) = 292 + 602 = 4441, f(4441) = 442 + 412 = 3617, etc. See 41)
29602 = 243 + 513 + 2053.
29602 = (22 + 4)(122 + 4)(862 + 4) = (22 + 4)(42 + 4)(2342 + 4).
Page of Squares : First Upload July 28, 2008 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2962
29622 = 313 + 1623 + 1653 = 813 + 1483 + 1713.
Page of Squares : First Upload July 28, 2008 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2964
29642 = (32 + 3)(62 + 3)(1372 + 3) = (42 + 3)(152 + 3)(452 + 3) = (42 + 3)(62 + 3)(72 + 3)(152 + 3).
The integral triangle of sides 4755, 5353, 9386 has square area 29642.
A, B, C, A+B, B+C, and C+A are squares for A = 29642, B = 91522, C = 94052.
Page of Squares : First Upload May 21, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2965
29655 = 229151913706853125 : 22 + 292 + 152 + 192 + 12 + 372 + 02 + 62 + 82 + 52 + 32 + 12 + 22 + 52 = 2965.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
2966
29662 = 8797156, 8 * 7 + 97 * 1 * 5 * 6 = 2966.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2969
29692 = 1043 + 1423 + 1693.
Page of Squares : First Upload July 28, 2008 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2972
29722 = 44 + 344 + 444 + 444.
1 / 2972 = 0.0003364...., and 3364 = 582.
Page of Squares : First Upload May 21, 2007 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2973
The square root of 2973 is 54.525...., and 54 = 52 + 22 + 52.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2975
29752 = 653 + 1403 + 1803.
29752 = (23 + 24 + 25 + 26 + ... + 57)2 + (58 + 59 + 60 + 61 + ... + 92)2.
29752 = (294 + 295 + 296 + 297 + 298 + 299 + 300)2 + (301 + 302 + 303 + 304 + 305 + 306 + 307)2.
Page of Squares : First Upload May 21, 2007 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2976
29762 = 923 + 1003 + 1923 = 923 + 1183 + 1863.
The square root of 2976 is 54.552...., and 54 = 52 + 52 + 22.
Page of Squares : First Upload May 21, 2007 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2977
793k + 1417k + 2977k + 11713k are squares for k = 1,2,3 (1302, 121942, 12793302).
Page of Squares : First Upload May 27, 2011 ; Last Revised May 27, 2011by Yoshio Mimura, Kobe, Japan
2978
29782 = 8868484, a square with 3 kinds of even digits (and a square pegged by 8).
29782 = 8868484, 82 + 82 + 62 + 82 + 42 + 82 + 42 = 182.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2979
29792 = 703 + 813 + 2003.
29792 = 8874441, a square with non-increasing digits.
Page of Squares : First Upload May 21, 2007 ; Last Revised July 28, 2008by Yoshio Mimura, Kobe, Japan
2982
2982 = (12 + 22 + 32 + ... + 352) / (12 + 22).
29822 = 353 + 1213 + 1923.
Page of Squares : First Upload July 28, 2008 ; Last Revised November 25, 2008by Yoshio Mimura, Kobe, Japan
2983
29832 = 8898289, a square with just 3 kinds of digits (a square pegged by 8).
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2984
29842 = 8904256, a square with different digits.
29842 = (12 + 7)(10552 + 7).
Page of Squares : First Upload May 21, 2007 ; Last Revised December 21, 2013by Yoshio Mimura, Kobe, Japan
2986
29862 = 8916196, a zigzag square.
1 / 2986 = 0.00033489..., and 33489 = 1832.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2987
29872 = 8922169, 89 + 2 * 21 * 69 = 2987.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2989
29892 = 8934121, a zigzag square.
29892 = 8934121, 8 * 93 * 4 + 12 + 1 = 2989.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2991
29912 = 8946081, a zigzag square.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2992
29922 = 8952064, a square with different digits.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2996
14k + 1162k + 1274k + 2450k are squares for k = 1,2,3 (702, 29962, 1354362).
Page of Squares : First Upload May 27, 2011 ; Last Revised May 27, 2011by Yoshio Mimura, Kobe, Japan
2997
(29972 - 3) = (22 - 3)(62 - 3)(72 - 3)(82 - 3)(102 - 3).
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2998
29982 = 8988004, 82 + 92 + 82 + 82 + 02 + 02 + 42 = 172.
Page of Squares : First Upload May 21, 2007 ; Last Revised May 21, 2007by Yoshio Mimura, Kobe, Japan
2999
2999 is the first prime for which the Legendre symbol (a/2999) = 1 for a = 1, 2,..., 12,
2999 is the second prime for which the Legendre symbol (a/2999) = 1 for a = 1, 2,..., 16.
by Yoshio Mimura, Kobe, Japan