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21000 - 21999

21000

1852 + 21000 = 2352, 1852 - 21000 = 1152,
1452 + 21000 = 2052, 1452 - 21000 = 52.

Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012
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, 2012
by 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, 2012
by 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, 2012
by 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, 2012
by Yoshio Mimura, Kobe, Japan

21033

210332 = (72 + 8)(192 + 8)(1452 + 8).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21050

210502 = 462465025, and 4624 = 682, 65025 = 2552.

Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012
by 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, 2012
by 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, 2012
by 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, 2013
by 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, 2012
by 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, 2012
by 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, 2012
by 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

Page of Squares : First Upload March 10, 2012 ; Last Revised February 8, 2014
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, 2012
by Yoshio Mimura, Kobe, Japan

21135

211352± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21144

211442 = (42 + 8)(43162 + 8).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21146

211462± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2012
by 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).

Page of Squares : First Upload March 10, 2012 ; Last Revised February 8, 2014
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, 2014
by Yoshio Mimura, Kobe, Japan

21177

211772± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2014
by 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, 2012
by 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, 2014
by 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, 2012
by 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, 2014
by Yoshio Mimura, Kobe, Japan

21230

212302± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2014
by 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, 2014
by Yoshio Mimura, Kobe, Japan

21264

212642± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2014
by 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, 2012
by 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).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
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).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
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, 2014
by Yoshio Mimura, Kobe, Japan

21332

213322± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2014
by 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, 2012
by 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).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
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, 2012
by Yoshio Mimura, Kobe, Japan

21402

214022 = (62 + 5)(472 + 5)(712 + 5).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2014
by Yoshio Mimura, Kobe, Japan

21435

214352± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2012
by 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, 2014
by 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, 2012
by Yoshio Mimura, Kobe, Japan

21492

214922± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21504

2002 + 21504 = 2482, 2002 - 21504 = 1362.

Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012
by Yoshio Mimura, Kobe, Japan

21546

215462± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21561

215612± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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).

Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012
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, 2012
by 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, 2012
by Yoshio Mimura, Kobe, Japan

21620

216202 = 467856900, and 467856 = 6842, 900 = 302.

Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012
by Yoshio Mimura, Kobe, Japan

21630

216302 = (32 + 6)(322 + 6)(1742 + 6).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21644

216442± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2014
by Yoshio Mimura, Kobe, Japan

21657

216572± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21663

216632± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21692

216922± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21705

217052± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21714

217142± 5 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2014
by 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, 2012
by Yoshio Mimura, Kobe, Japan

21748

217482± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21750

217502 = (72 + 9)(362 + 9)(792 + 9).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2014
by Yoshio Mimura, Kobe, Japan

21790

217902± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2012
by 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).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
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, 2012
by Yoshio Mimura, Kobe, Japan

21854

218542 = (372 + 3)(5902 + 3).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2012
by Yoshio Mimura, Kobe, Japan

21867

218672± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2012
by 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, 2012
by 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, 2012
by 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, 2012
by Yoshio Mimura, Kobe, Japan

21902

219022± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2012
by Yoshio Mimura, Kobe, Japan

21910

219102± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2014
by Yoshio Mimura, Kobe, Japan

21916

219162± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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).

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21941

219412 = 25142 + 25152 + 25162 + ... + 25872.

Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012
by Yoshio Mimura, Kobe, Japan

21945

219452± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by 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, 2013
by Yoshio Mimura, Kobe, Japan

21980

219802± 3 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

21999

219992± 2 are primes.

Page of Squares : First Upload February 8, 2014 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan