21000
1852 + 21000 = 2352, 1852 - 21000 = 1152,
1452 + 21000 = 2052, 1452 - 21000 = 52.
by Yoshio Mimura, Kobe, Japan
21001
210012 = 441042001 is a reversible square (100240144 = 100122).
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21002
210022 = 441084004 is a reversible square (400480144 = 200122).
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21011
210112 = 441462121 is a reversible square (121264144 = 110122).
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21021
210212 = 441882441 is a reversible square (144288144 = 120122).
210212 = 441882441, 484 = 222, 484 = 222, 121 = 112.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21033
210332 = (72 + 8)(192 + 8)(1452 + 8).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21050
210502 = 462465025, and 4624 = 682, 65025 = 2552.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21052
210522= 603 x 604 + 604 x 605 + 605 x 606 + ... + 1156 x 1157.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21078
210782 = 444282084 is a square which consists of even digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21079
210792 = 444324241, a square every digit of which is non-zero and smaller than 5.
Page of Squares : First Upload September 18, 2013 ; Last Revised September 18, 2013by Yoshio Mimura, Kobe, Japan
21101
211012 = 445252201 is a reversible square (102252544 = 101122).
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21102
211022 = 445294404 is a reversible square (404492544 = 201122).
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21111
211112 = 445674321 is a reversible square (123476544 = 111122).
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21120
211102 = (22 - 1)(32 - 1)(92 - 1)(212 - 1)(232 - 1) = (22 - 1)(92 - 1)(212 - 1)(652 - 1)
= (32 - 1)(312 - 1)(2412 - 1) = (52 - 1)(92 - 1)(212 - 1)(232 - 1).
2442 + 21120 = 2842, 2442 - 21120 = 1962,
1462 + 21120 = 2062, 1462 - 21120 = 142
by Yoshio Mimura, Kobe, Japan
21129
211292 = 446434641 is a square which is pegged by 4.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21135
211352± 2 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21144
211442 = (42 + 8)(43162 + 8).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21146
211462± 3 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21168
211682 = 448084224 is a square which consists of even digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21170
211702 = S2(872) + S2(879), where S2(n) = 12 + 22 + ... + n2.
211702 = (12 + 1)(122 + 1)(272 + 1)(462 + 1) = (172 + 1)(272 + 1)(462 + 1)
= (12 + 4)(52 + 4)(192 + 4)(922 + 4) = (42 + 9)(72 + 9)(82 + 9)(652 + 9).
by Yoshio Mimura, Kobe, Japan
21175
211752 = (12 + 6)(72 + 6)(292 + 6)(372 + 6).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21177
211772± 2 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21200
212002 = (12 + 4)(42 + 4)(62 + 4)(72 + 4)(462 + 4) = (42 + 4)(72 + 4)(142 + 4)(462 + 4).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21201
212012 = 441844601 is a reversible square (106448144 = 102122).
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21210
212102 = (12 + 6)(62 + 6)(142 + 6)(872 + 6).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21212
212122 = 449948944 is a square which contains only 3 kinds of digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21222
212222± 5 are primes.
212222 = (12 + 2)(42 + 2)(282 + 2)(1032 + 2).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21230
212302± 3 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21250
212502 = (12 + 9)(42 + 9)(292 + 9)(462 + 9) = (52 + 9)(462 + 9)(792 + 9).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21252
212522 = (222 - 1)(9672 - 1).
212522 = 8026 x 8027 + 8028 x 8029 + 8030 x 8031 + 8032 x 8033 + ... + 8038 x 8039.
Page of Squares : First Upload March 10, 2012 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21264
212642± 5 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21315
213152 = (12 + 6)(32 + 6)(92 + 6)(2232 + 6).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21316
21316 = 1462 is a zigzag square which is pegged by 1.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21318
213182 = (12 + 2)(22 + 2)(32 + 2)(242 + 2)(632 + 2) = (12 + 2)(32 + 2)(62 + 2)(242 + 2)(252 + 2)
= (12 + 2)(32 + 2)(62 + 2)(6022 + 2) = (12 + 2)(82 + 2)(242 + 2)(632 + 2)
= (142 + 2)(242 + 2)(632 + 2) = (32 + 2)(42 + 2)(242 + 2)(632 + 2) = (32 + 2)(442 + 2)(1462 + 2)
= (32 + 2)(62 + 2)(72 + 2)(1462 + 2).
by Yoshio Mimura, Kobe, Japan
21320
213202 = (12 + 4)(22 + 4)(232 + 4)(1462 + 4) = (12 + 4)(32 + 4)(182 + 4)(1462 + 4)
= (12 + 4)(32 + 4)(62 + 4)(182 + 4)(232 + 4) = (32 + 4)(142 + 4)(182 + 4)(232 + 4)
= (62 + 4)(232 + 4)(1462 + 4).
by Yoshio Mimura, Kobe, Japan
21328
213282 = (12 + 3)(112 + 3)(132 + 3)(732 + 3).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21332
213322± 3 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21344
213442 = (32 + 7)(42 + 7)(152 + 7)(732 + 7) = (152 + 7)(192 + 7)(732 + 7).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21366
213662 = 456505956 is a square which is pegged by 5.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21384
213842 = (12 + 8)(52 + 8)(282 + 8)(442 + 8) = (172 + 8)(282 + 8)(442 + 8)
= (42 + 8)(52 + 8)(172 + 8)(442 + 8).
by Yoshio Mimura, Kobe, Japan
21397
213972 = 457831609 is a square which consists of different digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21402
214022 = (62 + 5)(472 + 5)(712 + 5).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21420
214202 = (42 - 1)(72 - 1)(162 - 1)(502 - 1) = (82 - 1)(162 - 1)(1692 - 1).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21435
214352± 2 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21439
214392 = 459630721 is a square which consists of different digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21460
214602 = (12 + 1)(32 + 1)(412 + 1)(1172 + 1) = (122 + 4)(17642 + 4).
Page of Squares : First Upload November 9, 2013 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21468
214682 = 460875024 is a reversible square (420578064 = 205082).
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21492
214922± 5 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21504
2002 + 21504 = 2482, 2002 - 21504 = 1362.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21546
215462± 5 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21561
215612± 2 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21600
1502 + 21600 = 2102, 1502 - 21600 = 302.
216002 = (22 - 1)(32 - 1)(42 - 1)(52 - 1)(92 - 1)(262 - 1) = (22 - 1)(32 - 1)(92 - 1)(192 - 1)(262 - 1)
= (22 - 1)(52 - 1)(92 - 1)(112 - 1)(262 - 1) = (32 - 1)(42 - 1)(72 - 1)(112 - 1)(262 - 1)
= (42 - 1)(72 - 1)(262 - 1)(312 - 1) = (52 - 1)(92 - 1)(192 - 1)(262 - 1) = (172 - 1)(262 - 1)(492 - 1).
by Yoshio Mimura, Kobe, Japan
21602
216022 = 466646404 is a square which consists of 3 kinds of even digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21609
21609 = 1472 is a zigzag square which consists of different digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21620
216202 = 467856900, and 467856 = 6842, 900 = 302.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21630
216302 = (32 + 6)(322 + 6)(1742 + 6).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21644
216442± 3 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21648
216482 = (162 + 8)(222 + 8)(602 + 8) = (22 + 8)(602 + 8)(1042 + 8).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21657
216572± 2 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21663
216632± 2 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21692
216922± 3 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21705
217052± 2 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21714
217142± 5 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21735
217352 = (22 + 5)(202 + 5)(3602 + 5) = (82 + 5)(202 + 5)(1302 + 5).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21744
217442 = 472801536 is a square which consists of different digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21748
217482± 3 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21750
217502 = (72 + 9)(362 + 9)(792 + 9).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21756
217562 = (12 + 3)(22 + 3)(122 + 3)(162 + 3)(212 + 3) = (52 + 3)(122 + 3)(162 + 3)(212 + 3).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21790
217902± 3 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21801
218012 = 475283601 is a square which consists of different digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21840
218402 = (22 - 1)(62 - 1)(272 - 1)(792 - 1) = (32 - 1)(42 - 1)(62 - 1)(3372 - 1)
= (42 - 1)(142 - 1)(152 - 1)(272 - 1) = (42 - 1)(272 - 1)(2092 - 1) = (62 - 1)(112 - 1)(3372 - 1).
by Yoshio Mimura, Kobe, Japan
21849
the sum of (13x + 9)2 is 5173792, where 0< 13x + 9 <= 21849.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21854
218542 = (372 + 3)(5902 + 3).
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21863
the sum of (26x + 23)2 is 3663572, where 0 < 26x + 23 <= 21863.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21867
218672± 2 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21877
218772 = 478603129 is a square which consists of different digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21888
218882 = 4! + 5! + 6! + 6! + 6! + 8! + 8! + 12!
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21889
218892 = 1! + 6! + 7! + 8! + 8! + 8! + 12!.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21901
219012 = 479653801 is a square which consists of different digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21902
219022± 3 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21904
21904 = 1482 is a zigzag square which consists of different digits.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21910
219102± 3 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21912
219122± 5 are primes.
219122 = 4! + 5! + 7! + 8! + 9! + 9! + 9! + 12!.
Page of Squares : First Upload March 10, 2012 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21916
219162± 3 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21924
219242 = (12 + 5)(22 + 5)(32 + 5)(112 + 5)(712 + 5) = (12 + 5)(32 + 5)(112 + 5)(132 + 5)(162 + 5)
= (12 + 5)(32 + 5)(42 + 5)(72 + 5)(712 + 5) = (12 + 5)(72 + 5)(172 + 5)(712 + 5)
= (32 + 5)(72 + 5)(112 + 5)(712 + 5) = (22 - 1)(82 - 1)(282 - 1)(572 - 1).
by Yoshio Mimura, Kobe, Japan
21941
219412 = 25142 + 25152 + 25162 + ... + 25872.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
21945
219452± 2 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21970
219702 = (22 + 1)(52 + 1)(82 + 1)(2392 + 1) = (52 + 1)(182 + 1)(2392 + 1).
Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013by Yoshio Mimura, Kobe, Japan
21980
219802± 3 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan
21999
219992± 2 are primes.
Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014by Yoshio Mimura, Kobe, Japan