Squares:22000s

22001

22001² = 484044001 is a reversible square (10440484 = 10022²).

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22002

22002² = 484088004 is a reversible square (400880484 = 20022²)
which consists of 3 kinds of even digits.

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22011

22011² = 484484121 is a reversible square (121484484 = 11022²).

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22017

22017²± 2 are primes.

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

22020

22020, 22021, 22022, 22023, 22024 and 22025 are six consecutive integers having square factors (the first case).

Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

22022

22022²± 3 are primes.

22022² = 144³ + 145³ + 146³ + 147³ + ... + 220³.

Page of Squares : First Upload March 17, 2012 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

22025

22025² = 485100625, and 4 = 2², 85100625 = 9225².

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22032

22032² = (1² + 8)(2² + 8)(44² + 8)(48² + 8) = (1² + 8)(3² + 8)(8² + 8)(10² + 8)(20² + 8)
= (10² + 8)(44² + 8)(48² + 8) = (2² + 8)(3² + 8)(4² + 8)(8² + 8)(37² + 8)
= (2² + 8)(8² + 8)(20² + 8)(37² + 8) = (3² + 8)(8² + 8)(14² + 8)(44² + 8)
= (4² + 8)(8² + 8)(14² + 8)(37² + 8) = (4² + 8)(8² + 8)(530² + 8).

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

22038

22038²± 5 are primes.

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

22050

22050² = (1² + 6)(3² + 6)(6² + 6)(12² + 6)(27² + 6).

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

22073

The sum of consecutive primes 2 + 3 + 5 + 7 + 11 + ... + 22073 = 5063².

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22080

22080² = (3² - 1)(7² - 1)(24² - 1)(47² - 1).

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

22100

22100² = (1² + 1)(2² + 1)(3² + 1)(4² + 1)(5² + 1)(8² + 1)(13² + 1)
= (1² + 1)(2² + 1)(3² + 1)(8² + 1)(13² + 1)(21² + 1) = (1² + 1)(2² + 1)(4² + 1)(5² + 1)(7² + 1)(47² + 1)
= (1² + 1)(2² + 1)(7² + 1)(21² + 1)(47² + 1) = (1² + 1)(3² + 1)(13² + 1)(18² + 1)(21² + 1)
= (1² + 1)(3² + 1)(4² + 1)(21² + 1)(57² + 1) = (1² + 1)(3² + 1)(4² + 1)(5² + 1)(13² + 1)(18² + 1)
= (1² + 1)(3² + 1)(4² + 1)(7² + 1)(8² + 1)(21² + 1) = (1² + 1)(3² + 1)(8² + 1)(13² + 1)(47² + 1)
= (1² + 1)(4² + 1)(5² + 1)(13² + 1)(57² + 1) = (1² + 1)(4² + 1)(5² + 1)(7² + 1)(8² + 1)(13² + 1)
= (1² + 1)(7² + 1)(8² + 1)(13² + 1)(21² + 1) = (1² + 4)(3² + 4)(36² + 4)(76² + 4)
= (1² + 4)(3² + 4)(8² + 4)(9² + 4)(36² + 4) = (1² + 4)(4² + 4)(29² + 4)(76² + 4)
= (1² + 4)(4² + 4)(8² + 4)(9² + 4)(29² + 4) = (1² + 9)(2² + 9)(5² + 9)(11² + 9)(29² + 9)
= (1² + 9)(5² + 9)(29² + 9)(41² + 9) = (1² + 1)(13² + 1)(21² + 1)(57² + 1)
= (2² + 1)(3² + 1)(4² + 1)(5² + 1)(7² + 1)(21² + 1) = (2² + 1)(3² + 1)(5² + 1)(13² + 1)(47² + 1)
= (2² + 1)(5² + 1)(7² + 1)(13² + 1)(21² + 1) = (3² + 1)(4² + 1)(5² + 1)(7² + 1)(47² + 1)
= (3² + 1)(7² + 1)(21² + 1)(47² + 1) = (4² + 4)(9² + 4)(536² + 4) = (5² + 1)(7² + 1)(13² + 1)(47² + 1).

Page of Squares : First Upload November 9, 2013 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

22101

22101² = 488454201 is a reversible square (102454884 = 10122²).

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22102

22102² = 488498404 is a reversible square (404894884 = 20122²).

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22111

22111² = 488896321 is a reversible square (123698884 = 11122²).

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22115

22115² = 3103² + 3104² + 3105² + ... + 3152².

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22116

22116² = (1² + 3)(4² + 3)(15² + 3)(168² + 3).

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

22122

22122²± 5 are primes.

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

22125

22125²± 2 are primes.

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

22140

22140² = (1² + 5)(5² + 5)(35² + 5)(47² + 5) = (1² + 5)(5² + 5)(6² + 5)(7² + 5)(35² + 5).

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

22144

22144²± 3 are primes.

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

22155

22155²± 2 are primes.

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

22175

22175² = 491730625 is a square which consists of different digits.

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22176

170² + 22176 = 226², 170² - 22176 = 82².

22176² = (10² - 1)(23² - 1)(97² - 1) = (2² - 1)(13² - 1)(23² - 1)(43² - 1)
= (2² - 1)(3² - 1)(23² - 1)(197² - 1) = (2² - 1)(65² - 1)(197² - 1)
= (3² - 1)(8² - 1)(23² - 1)(43² - 1) = (5² - 1)(23² - 1)(197² - 1)
= (8² - 1)(43² - 1)(65² - 1).

Page of Squares : First Upload March 17, 2012 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

22217

22217² = 1036² + 1037² + 1038² + ... + 1373².

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22250

22250² = (1² + 4)(4² + 4)(11² + 4)(199² + 4).

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

22317

22317²± 2 are primes.

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

22320

22320² = (1² + 2³ + 3³ + 4²)(5² + 6³ + 7³ + ... + 12²)(13² + 14³ + 15³ + ... + 43²).

Page of Squares : First Upload February 9, 2013 ; Last Revised February 9, 2013
by Yoshio Mimura, Kobe, Japan

22330

22330² = 225³ + 226³ + 227³ + 228³ + ... + 259³.

22330² = (1² + 6)(4² + 6)(13² + 6)(136² + 6) - (1² + 6)(62² + 6)(136² + 6)
= (1² + 6)(7² + 6)(8² + 6)(136² + 6) = (20² + 6)(29² + 6)(38² + 6)
= (4² + 6)(38² + 6)(125² + 6) = (7² + 6)(22² + 6)(136² + 6).

Page of Squares : First Upload March 17, 2012 ; Last Revised February 8, 2014
by Yoshio Mimura, Kobe, Japan

22338

22338² = (1² + 2)(2² + 2)(7² + 2)(12² + 2)(61² + 2) = (4² + 2)(7² + 2)(12² + 2)(61² + 2).

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

22344

22344² = (1² + 3)(12² + 3)(15² + 3)(61² + 3) = (1² + 3)(2² + 3)(12² + 3)(15² + 3)(23² + 3)
= (1² + 3)(2² + 3)(3² + 3)(4² + 3)(12² + 3)(23² + 3)
= (1² + 3)(2² + 3)(4² + 3)(5² + 3)(12² + 3)(15² + 3)
= (1² + 3)(3² + 3)(4² + 3)(12² + 3)(61² + 3) = (1² + 3)(4² + 3)(9² + 3)(12² + 3)(23² + 3)
= (2² + 3)(3² + 3)(4² + 3)(15² + 3)(37² + 3) = (2² + 3)(3² + 3)(4² + 3)(9² + 3)(61² + 3)
= (2² + 3)(9² + 3)(15² + 3)(61² + 3) = (3² + 3)(4² + 3)(5² + 3)(12² + 3)(23² + 3)
= (4² + 3)(9² + 3)(15² + 3)(37² + 3) = (5² + 3)(12² + 3)(15² + 3)(23² + 3).

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

22414

22414²= 1502 x 1503 + 1503 x 1504 + 1504 x 1505 +...+ 1697 x 1698.

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22428

22428² = (1² + 5)(3² + 5)(7² + 5)(333² + 5).

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

22440

157² + 22440 = 217², 157² - 22440 = 47².

22440² = (16² - 1)(21² - 1)(67² - 1).

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22446

22446² = (9² + 5)(34² + 5)(71² + 5).

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

22456

22456² = 504271936 is a square with different digits.

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22464

22464² = (17² - 1)(25² - 1)(53² - 1).

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

22466

22466² = 966² + 967² + 968² + 969² + ... + 1341².

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22482

22482²± 5 are primes.

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

22490

22490² = (1² + 9)(67² + 9)(106² + 9).

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

22500

22500² = (1² + 9)(3² + 9)(21² + 9)(79² + 9).

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

22504

22504² = (2² + 4)(53² + 4)(150² + 4).

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

22512

22512² = (1² + 3)(3² + 3)(5² + 3)(8² + 3)(75² + 3).

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

22525

22525² = (4² + 1)(30² + 1)(182² + 1).

Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013
by Yoshio Mimura, Kobe, Japan

22528

22528² = (1² + 7)(11² + 7)(13² + 7)(53² + 7) = (1² + 7)(2² + 7)(13² + 7)(181² + 7)
= (1² + 7)(2² + 7)(3² + 7)(11² + 7)(53² + 7) = (1² + 7)(2² + 7)(3² + 7)(5² + 7)(9² + 7)(11² + 7)
= (1² + 7)(3² + 7)(5² + 7)(11² + 7)(31² + 7) = (1² + 7)(5² + 7)(9² + 7)(11² + 7)(13² + 7)
= (1² + 7)(9² + 7)(11² + 7)(75² + 7) = (2² + 7)(3² + 7)(9² + 7)(181² + 7)
= (3² + 7)(31² + 7)(181² + 7) = (3² + 7)(5² + 7)(13² + 7)(75² + 7)
= (3² + 7)(9² + 7)(11² + 7)(53² + 7) = (5² + 7)(53² + 7)(75² + 7) = (9² + 7)(13² + 7)(181² + 7).

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

22568

22568² = (1² + 3)(2² + 3)(11² + 3)(19² + 3)(20² + 3) = (1² + 3)(2² + 3)(11² + 3)(383² + 3)
= (1² + 3)(7² + 3)(19² + 3)(82² + 3) = (2² + 3)(5² + 3)(7² + 3)(11² + 3)(20² + 3)
= (5² + 3)(11² + 3)(19² + 3)(20² + 3) = (5² + 3)(11² + 3)(383² + 3).

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

22572

22572² = (1² + 2)(2² + 2)(3² + 2)(6² + 2)(8² + 2)(32² + 2)
= (1² + 2)(2² + 2)(4² + 2)(6² + 2)(8² + 2)(25² + 2) = (1² + 8)(2² + 8)(17² + 8)(126² + 8)
= (1² + 8)(2² + 8)(26² + 8)(83² + 8) = (1² + 8)(2² + 8)(5² + 8)(7² + 8)(50² + 8)
= (1² + 8)(5² + 8)(10² + 8)(126² + 8) = (1² + 8)(5² + 8)(26² + 8)(50² + 8)
= (1² + 8)(5² + 8)(6² + 8)(7² + 8)(26² + 8) = (1² + 8)(7² + 8)(26² + 8)(38² + 8)
= (2² + 2)(3² + 2)(4² + 2)(6² + 2)(8² + 2)(13² + 2)
= (2² + 2)(3² + 2)(6² + 2)(14² + 2)(32² + 2) = (2² + 2)(4² + 2)(6² + 2)(14² + 2)(25² + 2)
= (2² + 2)(6² + 2)(8² + 2)(13² + 2)(14² + 2) = (10² + 8)(17² + 8)(126² + 8)
= (2² + 2)(6² + 2)(8² + 2)(184² + 2) = (2² + 8)(7² + 8)(10² + 8)(83² + 8)
= (2² + 8)(7² + 8)(17² + 8)(50² + 8) = (3² + 2)(4² + 2)(6² + 2)(8² + 2)(32² + 2)
= (5² + 8)(7² + 8)(10² + 8)(50² + 8) = (6² + 2)(8² + 2)(14² + 2)(32² + 2)
= (6² + 8)(7² + 8)(17² + 8)(26² + 8) = (10² + 8)(26² + 8)(83² + 8) = (17² + 8)(26² + 8)(50² + 8).

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

22608

22608²± 5 are primes.

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

22630

22630²± 3 are primes.

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

22638

22638² = (1² + 6)(4² + 6)(15² + 6)(120² + 6) = (6² + 6)(29² + 6)(120² + 6).

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

22660

22660² = 1028² + 1029² + 1030² + 1031² + ... + 1379².

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22680

159² + 22680 = 219², 159² - 22680 = 51².

22680² = (2² - 1)(3² - 1)(19² - 1)(244² - 1) = (2² - 1)(3² - 1)(4² - 1)(5² - 1)(244² - 1)
= (2² - 1)(5² - 1)(11² - 1)(244² - 1) = (2² - 1)(5² - 1)(8² - 1)(13² - 1)(26² - 1)
= (5² - 1)(19² - 1)(244² - 1).

22680² = (1³ + 2³ + 3³ + 4³ + 5³)(6³)(7³ + 8³ + 9³ + ... + 14³).

Page of Squares : First Upload March 17, 2012 ; Last Revised February 9, 2013
by Yoshio Mimura, Kobe, Japan

22692

22692²± 5 are primes.

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

22704

22704² = (2² + 8)(32² + 8)(204² + 8).

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

22770

22770² = (3³ + 9)(6³ + 9)(40³ + 9).

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

22781

22781² = 1! + 5! + 7! + 7! + 7! + 8! + 11! + 12!.

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22785

22785² = (1² + 6)(5² + 6)(27² + 6)(57² + 6).

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

22800

22800² = (4² - 1)(39² - 1)(151² - 1).

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

22802

22802²± 3 are primes.

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

22815

22815²± 2 are primes.

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

22826

22826²± 3 are primes.

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

22836

22836² = 206*207*208 + 208*209*210 + 210*211*212 + 212*213*214 + ... + 276*277*278.

Page of Squares : First Upload October 26, 2103 ; Last Revised October 26, 2103
by Yoshio Mimura, Kobe, Japan

22840

22815²± 3 are primes.

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

22848

22848² = (3² - 1)(5² - 1)(33² - 1)(50² - 1).

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

22862

22862²± 3 are primes.

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

22865

22865² = 522808225 is a palindromic square.

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22869

A cubic equation :
(X + 1128²)(X + 2464²)(X + 22869²) = X³ + 23029²X² + 62035512²X + 63561915648².

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22887

22887² = 523814769 is a square with different digits.

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22925

22925² = 525555625 is a square with 3 kinds of digits.

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22932

22932² = (2² + 3)(3² + 3)(6² + 3)(12² + 3)(33² + 3) = (6² + 3)(9² + 3)(12² + 3)(33² + 3).

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

22939

22939² = (14² + 7)(1610² + 7).

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

22946

22946²± 3 are primes.

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

22950

22950² = (1² + 9)(6² + 9)(9² + 9)(114² + 9) = (3² + 9)(4² + 9)(9² + 9)(114² + 9)
= (3² + 9)(9² + 9)(12² + 9)(46² + 9) = (4² + 9)(5² + 9)(6² + 9)(9² + 9)(12² + 9)
= (4² + 9)(9² + 9)(12² + 9)(39² + 9) = (6² + 9)(9² + 9)(12² + 9)(29² + 9)
= (9² + 9)(21² + 9)(114² + 9).

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

22962

22962² = S2(908) + S2(940), where S2(n) = 1² + 2² + 3² + ... + n².

Page of Squares : First Upload March 17, 2012 ; Last Revised March 17, 2012
by Yoshio Mimura, Kobe, Japan

22971

22971² = (4² + 3)(6² + 3)(20² + 3)(42² + 3).

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