Squares:97000s

97011

97011²± 2 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97020

97020² = 970*971*972 + 972*973*974 + 974*975*976 + 976*977*978 + ... + 988*989*990.

Page of Squares : First Upload October 26, 2013 ; Last Revised October 26, 2013
by Yoshio Mimura, Kobe, Japan

97042

97042²± 3 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97080

The quadratic polynomial 97080X² - 560880X + 1167721 takes the values 839², 659², 599², 691², 889², 1139² at X = 1, 2,..., 6.

Page of Squares : First Upload January 5, 2013 ; Last Revised January 5, 2013
by Yoshio Mimura, Kobe, Japan

97092

97092²± 5 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97104

425² + 97104 = 527², 425² - 97104 = 289².

Page of Squares : First Upload January 5, 2013 ; Last Revised January 5, 2013
by Yoshio Mimura, Kobe, Japan

97150

97150²= 554 x 555 + 555 x 556 + 556 x 557 +...+ 3053 x 3054.

Page of Squares : First Upload January 5, 2013 ; Last Revised January 5, 2013
by Yoshio Mimura, Kobe, Japan

97162

97162² = (6² + 1)(31² + 1)(515² + 1).

Page of Squares : First Upload November 16, 2013 ; Last Revised November 16, 2013
by Yoshio Mimura, Kobe, Japan

97223

97223² = 3752² + 3753² + 3754² + ... + 4329².

Page of Squares : First Upload January 5, 2013 ; Last Revised January 5, 2013
by Yoshio Mimura, Kobe, Japan

97264

97264²± 3 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97278

97278²± 5 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97284

97284² = (5² + 8)(6² + 8)(27² + 8)(94² + 8) = (27² + 8)(38² + 8)(94² + 8).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97310

97310²± 3 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97335

97335² = (10² + 5)(20² + 5)(472² + 5).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97348

97348² = 9888² + 9889² + 9890² + ... + 9983².

Page of Squares : First Upload January 5, 2013 ; Last Revised January 5, 2013
by Yoshio Mimura, Kobe, Japan

97350

97350² = (3² + 6)(4² + 6)(7² + 6)(17² + 6)(42² + 6) = (3² + 6)(4² + 6)(17² + 6)(312² + 6)
= (7² + 6)(17² + 6)(18² + 6)(42² + 6) = (7² + 6)(42² + 6)(312² + 6) = (17² + 6)(18² + 6)(312² + 6).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97356

97356² = (1² + 3)(2² + 3)(3² + 3)(34² + 3)(156² + 3)
= (1² + 3)(2² + 3)(4² + 3)(27² + 3)(156² + 3) = (1² + 3)(4² + 3)(12² + 3)(27² + 3)(34² + 3)
= (1² + 3)(9² + 3)(34² + 3)(156² + 3) = (2² + 3)(4² + 3)(9² + 3)(27² + 3)(34² + 3)
= (3² + 3)(5² + 3)(34² + 3)(156² + 3) = (4² + 3)(5² + 3)(27² + 3)(156² + 3)
= (23² + 3)(27² + 3)(156² + 3).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97392

97392²± 5 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97416

97416² = (1² + 8)(4² + 8)(5² + 8)(19² + 8)(60² + 8) = (1² + 8)(16² + 8)(19² + 8)(104² + 8)
= (1² + 8)(19² + 8)(28² + 8)(60² + 8) = (4² + 8)(17² + 8)(19² + 8)(60² + 8)
= (5² + 8)(8² + 8)(19² + 8)(104² + 8) = (2² - 1)(3² - 1)(122² - 1)(163² - 1)
= (5² - 1)(122² - 1)(163² - 1).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97440

842² + 97440 = 898², 842² - 97440 = 782².

97440² = (2² - 1)(3² - 1)(6² - 1)(57² - 1)(59² - 1) = (2² - 1)(3² - 1)(57² - 1)(349² - 1)
= (4² - 1)(15² - 1)(1681² - 1) = (5² - 1)(6² - 1)(57² - 1)(59² - 1) = (5² - 1)(57² - 1)(349² - 1)
= (6² - 1)(57² - 1)(289² - 1) = (29² - 1)(57² - 1)(59² - 1).

Page of Squares : First Upload January 5, 2013 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97441

The quadratic polynomial 97441X² - 636470X + 1048825 takes the values 714², 407², 128², 249², 550², 859² at X = 1, 2,..., 6.

Page of Squares : First Upload January 5, 2013 ; Last Revised January 5, 2013
by Yoshio Mimura, Kobe, Japan

97500

97500² = (1² + 9)(2² + 9)(9² + 9)(11² + 9)(79² + 9) = (1² + 9)(9² + 9)(41² + 9)(79² + 9).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97524

97524² = (1² + 5)(2² + 5)(3² + 5)(7² + 5)(9² + 5)(52² + 5)
= (1² + 5)(2² + 5)(3² + 5)(9² + 5)(11² + 5)(34² + 5)
= (1² + 5)(3² + 5)(4² + 5)(7² + 5)(9² + 5)(34² + 5) = (1² + 5)(7² + 5)(9² + 5)(11² + 5)(52² + 5)
= (1² + 5)(7² + 5)(9² + 5)(17² + 5)(34² + 5) = (3² + 5)(7² + 5)(9² + 5)(11² + 5)(34² + 5).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97552

97552²± 3 are primes.

97552² = (1² + 3)(2² + 3)(5² + 3)(7² + 3)(8² + 3)(59² + 3)
= (1² + 3)(5² + 3)(8² + 3)(19² + 3)(59² + 3).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97556

97556² = 9517173136, 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

97615

97615² = (13² + 6)(7379² + 6).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97638

97638²± 5 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97642

(97642² + 8) = (5² + 8)(9² + 8)(10² + 8)(11² + 8)(15² + 8)
= (1² + 8)(2² + 8)(5² + 8)(9² + 8)(11² + 8)(15² + 8)

Page of Squares : First Upload January 5, 2013 ; Last Revised January 5, 2013
by Yoshio Mimura, Kobe, Japan

97650

97650² = (3² + 6)(5² + 6)(6² + 6)(12² + 6)(57² + 6) = (3² + 6)(12² + 6)(36² + 6)(57² + 6).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97684

97684²± 3 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97686

97686² = (1² + 2)(2² + 2)(5² + 2)(20² + 2)(221² + 2) = (4² + 2)(5² + 2)(20² + 2)(221² + 2)
= (20² + 2)(22² + 2)(221² + 2).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97692

97692²± 5 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97773

97773² = 9559559529, a square with 3 kinds of digits.

Page of Squares : First Upload January 5, 2013 ; Last Revised January 5, 2013
by Yoshio Mimura, Kobe, Japan

97779

97779² = 9560732841, a square with different digits.

Page of Squares : First Upload January 5, 2013 ; Last Revised January 5, 2013
by Yoshio Mimura, Kobe, Japan

97790

97790² = (1² + 6)(8² + 6)(11² + 6)(392² + 6) = (2² + 6)(4² + 6)(6593² + 6)
= (2² + 6)(7² + 6)(11² + 6)(370² + 6) = (11² + 6)(22² + 6)(392² + 6).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97866

97866²± 5 are primes.

97866² = 9577753956, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97872

97872² = 1067² + 1068² + 1069² + ... + 3105².

Page of Squares : First Upload January 5, 2013 ; Last Revised January 5, 2013
by Yoshio Mimura, Kobe, Japan

97876

97876² = 9579711376, 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

97856

97956² = 9595377936, 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

97908

97908²± 5 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97920

97920² = (2² - 1)(17² - 1)(33² - 1)(101² - 1) = (2² - 1)(3² - 1)(4² - 1)(9² - 1)(577² - 1)
= (2² - 1)(7² - 1)(16² - 1)(511² - 1) = (2² - 1)(9² - 1)(11² - 1)(577² - 1)
= (2² - 1)(33² - 1)(35² - 1)(49² - 1) = (3² - 1)(4² - 1)(16² - 1)(17² - 1)(33² - 1)
= (3² - 1)(4² - 1)(33² - 1)(271² - 1) = (3² - 1)(7² - 1)(9² - 1)(16² - 1)(35² - 1)
= (4² - 1)(5² - 1)(9² - 1)(577² - 1) = (9² - 1)(19² - 1)(577² - 1) = (11² - 1)(16² - 1)(17² - 1)(33² - 1)
= (11² - 1)(33² - 1)(271² - 1).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97959

97959²± 2 are primes.

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan

97966

97966² = 9597337156, 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

97969

97969 = 313², a zigzag square pegged by 9.

Page of Squares : First Upload January 5, 2013 ; Last Revised January 5, 2013
by Yoshio Mimura, Kobe, Japan

97970

97970² = (1² + 1)(10² + 1)(22² + 1)(313² + 1).

Page of Squares : First Upload November 16, 2013 ; Last Revised November 16, 2013
by Yoshio Mimura, Kobe, Japan

97976

97976² = (17² + 7)(18² + 7)(313² + 7).

Page of Squares : First Upload April 16, 2014 ; Last Revised April 16, 2014
by Yoshio Mimura, Kobe, Japan