Squares:37000s

37000

37000² = (1² + 4)(6² + 4)(11² + 4)(234² + 4) = (11² + 4)(14² + 4)(234² + 4).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37026

37026² = (1² + 2)(3² + 2)(14² + 2)(19² + 2)(24² + 2) = (3² + 2)(7² + 2)(8² + 2)(10² + 2)(19² + 2)
= (3² + 2)(10² + 2)(19² + 2)(58² + 2).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37034

37034² = 1371517156, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

37044

37044² = (1² + 5)(3² + 5)(7² + 5)(17² + 5)(32² + 5).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37059

37059²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37060

37060² = (1² + 1)(3² + 1)(33² + 1)(251² + 1).

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

37086

37086² = 1375371396, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

37094

37094²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37134

37134²± 5 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37149

37149²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37156

37156²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37158

37158²± 5 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37164

37164² = 808² + 809² + 810² + ... + 1671².

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37176

37176² = 1382054976, a square with different digits.

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37204

37204²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37246

37246²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37249

37249 = 193², a square with different digits.

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37260

37260² = (1² + 5)(2² + 5)(5² + 5)(7² + 5)(8² + 5)(15² + 5)
= (1² + 5)(2² + 5)(5² + 5)(15² + 5)(61² + 5) = (5² + 5)(7² + 5)(15² + 5)(61² + 5).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37281

37281²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37292

37292²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37296

37296² = (2² - 1)(73² - 1)(295² - 1).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37312

37312² = (1² + 7)(2² + 7)(5² + 7)(24² + 7)(29² + 7) = (1² + 7)(29² + 7)(453² + 7)
= (3² + 7)(13² + 7)(24² + 7)(29² + 7) = (5² + 7)(9² + 7)(24² + 7)(29² + 7)
= (24² + 7)(29² + 7)(53² + 7).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37338

37338² = (3² + 5)(9979² + 5).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37345

37345² = 568² + 569² + 570² + ... + 1634².

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37352

37352²± 3 are primes.

37352² = (4² + 7)(7² + 7)(14² + 7)(73² + 7).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37431

37431²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37440

194² + 37440 = 274², 194² - 37440 = 14².

37440² = (2² - 1)(3² - 1)(4² - 1)(25² - 1)(79² - 1) = (2² - 1)(3² - 1)(7² - 1)(14² - 1)(79² - 1)
= (2² - 1)(7² - 1)(9² - 1)(14² - 1)(25² - 1) = (2² - 1)(11² - 1)(25² - 1)(79² - 1)
= (2² - 1)(17² - 1)(25² - 1)(51² - 1) = (3² - 1)(5² - 1)(51² - 1)(53² - 1)
= (4² - 1)(5² - 1)(25² - 1)(79² - 1) = (5² - 1)(7² - 1)(14² - 1)(79² - 1)
= (9² - 1)(53² - 1)(79² - 1) = (19² - 1)(25² - 1)(79² - 1).

Page of Squares : First Upload June 30 2012 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37444

37444² = (3² + 7)(20² + 7)(464² + 7) = (4² + 7)(20² + 7)(387² + 7).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37450

37450² = (2² + 6)(23² + 6)(512² + 6).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37464

37464² = (1² + 3)(3² + 3)(9² + 3)(590² + 3).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37473

37473² = 1404225729, with 1404225 = 1185² and 729 = 27².

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37485

37485² = (6² - 1)(8² - 1)(16² - 1)(50² - 1).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37500

37500² = (1³ + 2³ + 3³ + ... + 24³)(25³).

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

37515

37515²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37521

37521² = (1² + 2)(3² + 2)(5² + 2)(1257² + 2).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37536

37536737536 = 193744².

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37544

37544²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37557

37557² = 1872² + 1873² + 1874² + ... + 2209².

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37569

The quadratic polynomial 37569X² - 275814X + 514921 takes the values 526², 337², 160², 113², 274², 461², 652² at X = 1, 2,..., 7,

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37570

37570²= 5184 x 5185 + 5185 x 5186 + 5186 x 5187 +...+ 5235 x 5236.

37570² = (1² + 1)(4² + 1)(8² + 1)(21² + 1)(38² + 1) = (2² + 1)(4² + 1)(5² + 1)(21² + 1)(38² + 1)
= (21² + 1)(38² + 1)(47² + 1) = (4² + 1)(5² + 1)(38² + 1)(47² + 1) = (1² + 9)(11² + 9)(1042² + 9).

Page of Squares : First Upload June 30 2012 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37587

37587² = (5² + 8)(27² + 8)(241² + 8).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37598

37598² = 1203² + 1205² + 1207² + 1209² + ... + 2169².

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37599

37599²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37620

37620² = (2² - 1)(10² - 1)(39² - 1)(56² - 1).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37636

37636 = 194² is a square with 3 kinds of digits.

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37638

37638² = (1² + 2)(2² + 2)(5² + 2)(24² + 2)(71² + 2) - (1² + 2)(2² + 2)(7² + 2)(11² + 2)(112² + 2)
= (1² + 2)(4² + 2)(7² + 2)(10² + 2)(71² + 2) = (1² + 2)(10² + 2)(11² + 2)(194² + 2)
= (1² + 2)(112² + 2)(194² + 2) = (2² + 2)(7² + 2)(11² + 2)(194² + 2)
= (4² + 2)(5² + 2)(24² + 2)(71² + 2) = (4² + 2)(7² + 2)(11² + 2)(112² + 2)
= (22² + 2)(24² + 2)(71² + 2).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37642

37642² = 2651 x 2652 + 2653 x 2654 + 2655 x 2656 + 2657 x 2658 + ... + 3003 x 3004.

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37664

37664² = (1² + 7)(2² + 7)(3² + 7)(10² + 7)(97² + 7) = (1² + 7)(10² + 7)(13² + 7)(97² + 7)
= (2² + 7)(9² + 7)(10² + 7)(117² + 7) = (2² + 7)(10² + 7)(11² + 7)(97² + 7)
= (2² + 7)(97² + 7)(117² + 7) = (3² + 7)(9² + 7)(10² + 7)(97² + 7) = (10² + 7)(31² + 7)(117² + 7).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37700

37700² = (1² + 1)(2² + 1)(3² + 1)(5² + 1)(18² + 1)(41² + 1) = (1² + 1)(2² + 1)(5² + 1)(41² + 1)(57² + 1)
= (1² + 1)(2² + 1)(5² + 1)(7² + 1)(8² + 1)(41² + 1) = (1² + 1)(2² + 1)(7² + 1)(17² + 1)(99² + 1)
= (1² + 1)(3² + 1)(5² + 1)(8² + 1)(12² + 1)(17² + 1) = (1² + 1)(3² + 1)(7² + 1)(12² + 1)(99² + 1)
= (1² + 1)(3² + 1)(7² + 1)(17² + 1)(70² + 1) = (1² + 1)(5² + 1)(17² + 1)(307² + 1)
= (1² + 1)(5² + 1)(7² + 1)(18² + 1)(41² + 1) = (3² + 1)(5² + 1)(41² + 1)(57² + 1)
= (3² + 1)(5² + 1)(7² + 1)(8² + 1)(41² + 1) = (3² + 1)(7² + 1)(17² + 1)(99² + 1)
= (1² + 4)(3² + 4)(5² + 4)(24² + 4)(36² + 4) = (1² + 4)(4² + 4)(5² + 4)(24² + 4)(29² + 4)
= (4² + 4)(5² + 4)(11² + 4)(140² + 4) = (11² + 4)(24² + 4)(140² + 4).

Page of Squares : First Upload November 9, 2013 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37739

37739² = 1424232121, 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

37758

37758² = (5² + 6)(9² + 6)(20² + 6)(36² + 6).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37779

37779²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37800

37800² = (2² - 1)(3² - 1)(4² - 1)(6² - 1)(13² - 1)(26² - 1)
= (2² - 1)(3² - 1)(4² - 1)(8² - 1)(251² - 1) = (2² - 1)(5² - 1)(6² - 1)(26² - 1)(29² - 1)
= (2² - 1)(6² - 1)(11² - 1)(13² - 1)(26² - 1) = (2² - 1)(8² - 1)(11² - 1)(251² - 1)
= (3² - 1)(6² - 1)(8² - 1)(11² - 1)(26² - 1) = (4² - 1)(5² - 1)(6² - 1)(13² - 1)(26² - 1)
= (4² - 1)(5² - 1)(8² - 1)(251² - 1) = (4² - 1)(6² - 1)(8² - 1)(11² - 1)(19² - 1)
= (4² - 1)(13² - 1)(26² - 1)(29² - 1) = (6² - 1)(8² - 1)(26² - 1)(31² - 1)
= (6² - 1)(13² - 1)(19² - 1)(26² - 1) = (8² - 1)(19² - 1)(251² - 1).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37829

37829² = 1805² + 1806² + 1807² + ... + 2166².

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37830

37830² = (9² + 9)(31² + 9)(128² + 9).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37832

37832²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37842

37842²± 5 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37880

37880²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37893

37893²± 2 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37898

37898²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37905

37905² = 1436789025, a square with different digits.

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37906

37906²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37926

37926² = (1² + 5)(9² + 5)(32² + 5)(52² + 5) = (3² + 5)(9² + 5)(32² + 5)(34² + 5)
= (4² + 5)(9² + 5)(17² + 5)(52² + 5).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37960

37960² = (3² + 4)(10² + 4)(19² + 4)(54² + 4).

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37961

37961² = 1! + 6! + 8! + 9! + 10! + 12! + 12! + 12!.

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37962

37962² = 1441113444, a square with 3 kinds of digits 1,3,4.

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan

37972

37972²± 3 are primes.

Page of Squares : First Upload February 28, 2014 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

37999

S2(37999) = S2(55) * S2(987), where S2(n) = 1² + 2² + 3² + ... + n².

Page of Squares : First Upload June 30 2012 ; Last Revised June 30, 2012
by Yoshio Mimura, Kobe, Japan