Squares:57000s

57005

57005² = 3249570025, and 3249 = 57², 570025 = 755².

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

57024

57024² = (1² + 8)(2² + 8)(4² + 8)(6² + 8)(10² + 8)(16² + 8)
= (1² + 8)(4² + 8)(8² + 8)(16² + 8)(28² + 8) = (2² + 8)(4² + 8)(5² + 8)(6² + 8)(8² + 8)(10² + 8)
= (2² + 8)(4² + 8)(8² + 8)(10² + 8)(38² + 8) = (2² + 8)(6² + 8)(8² + 8)(10² + 8)(28² + 8)
= (7² - 1)(17² - 1)(485² - 1).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57036

57036² = (1² + 3)(2² + 3)(5² + 3)(12² + 3)(168² + 3) = (2² + 3)(3² + 3)(37² + 3)(168² + 3)
= (9² + 3)(37² + 3)(168² + 3).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57057

57057²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57072

57072² = (17² - 1)(3363² - 1).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57105

57105²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57112

57112² = 1910² + 1911² + 1912² + ... + 2558².

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

57120

298² + 57120 = 382², 298² - 57120 = 178².

57120, 57121, 57122, 57123, 57124 and 57125 are six consecutive integers having square factors (the 6th case).

57120² = (2² - 1)(3² - 1)(69² - 1)(169² - 1) = (2² - 1)(6² - 1)(33² - 1)(169² - 1)
= (4² - 1)(9² - 1)(33² - 1)(50² - 1) = (5² - 1)(69² - 1)(169² - 1) = (15² - 1)(16² - 1)(239² - 1)
= (99² - 1)(577² - 1).

Page of Squares : First Upload September 15, 2012 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57121

57121 = 239² is a zigzag square.

1 + 2 + 3 + ... + 57121 = 1² - 2² + 3² - 4² + ... + 57121² = 40391².

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

57130

57130² = (41² + 1)(1393² + 1) = (1² + 4)(5² + 4)(28² + 4)(169² + 4).

Page of Squares : First Upload November 16, 2013 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57158

57158²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57168

57168²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57190

57190²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57198

57198²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57222

57222² = (1² + 2)(3² + 2)(7² + 2)(24² + 2)(58² + 2) = (1² + 2)(3² + 2)(10² + 2)(24² + 2)(41² + 2)
= (1² + 2)(7² + 2)(10² + 2)(19² + 2)(24² + 2) = (2² + 2)(3² + 2)(7² + 2)(24² + 2)(41² + 2)
= (7² + 2)(8² + 2)(24² + 2)(41² + 2) = (24² + 2)(41² + 2)(58² + 2).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57236

57236²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57252

57252²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57321

57321² = 3285697041 is a square with different digits.

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

57342

57342²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57387

57387²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57410

57410² = (2² + 1)(3² + 1)(8119² + 1) = (7² + 1)(8119² + 1).

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

57424

57424² = 629² + 630² + 631² + ... + 2164².

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

57426

57426²± 5 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57442

57442²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57456

57456² = (2² - 1)(8² - 1)(37² - 1)(113² - 1).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57460

57460² = (1² + 1)(3² + 1)(4² + 1)(13² + 1)(239² + 1) = (1² + 1)(5² + 1)(8² + 1)(21² + 1)(47² + 1).

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

57477

57477²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57512

57512² = (1² + 3)(2² + 3)(7² + 3)(32² + 3)(47² + 3) = (1² + 3)(19² + 3)(32² + 3)(47² + 3)
= (5² + 3)(7² + 3)(32² + 3)(47² + 3).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57544

57544² = 3311311936, 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

57600

57600² = (2² - 1)(3² - 1)(4² - 1)(7² - 1)(9² - 1)(49² - 1)
= (2² - 1)(3² - 1)(4² - 1)(9² - 1)(11² - 1)(31² - 1) = (2² - 1)(7² - 1)(9² - 1)(11² - 1)(49² - 1)
= (3² - 1)(4² - 1)(9² - 1)(19² - 1)(31² - 1) = (4² - 1)(5² - 1)(7² - 1)(9² - 1)(49² - 1)
= (4² - 1)(5² - 1)(9² - 1)(11² - 1)(31² - 1) = (7² - 1)(9² - 1)(19² - 1)(49² - 1)
= (9² - 1)(11² - 1)(19² - 1)(31² - 1).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57618

57618² = 49³ + 50³ + 51³ + ... + 339³.

57618² = (2² + 2)(3² + 2)(5² + 2)(17² + 2)(80² + 2) = (5² + 2)(8² + 2)(17² + 2)(80² + 2).

Page of Squares : First Upload September 15, 2012 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57624

245² + 57624 = 343², 245² - 57624 = 49².

57624² = (2² + 3)(5² + 3)(9² + 3)(12² + 3)(37² + 3).

Page of Squares : First Upload September 15, 2012 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57645

57645²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57665

57665² = 3325252225 is a square of 3 kinds of digits.

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

57672

57672² = (1² + 8)(44² + 8)(436² + 8).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57681

57681² = (12² + 9)(22² + 9)(210² + 9).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57693

57693²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57694

57694²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57722

57722² = (2² + 3)(4² + 3)(61² + 3)(82² + 3).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57735

57735² = 3333330225, a square contains repeating digits.

Page of Squares : First Upload September 18, 2013 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

57750

57750² = (1² + 6)(2² + 6)(3² + 6)(6² + 6)(7² + 6)(37² + 6)
= (1² + 6)(2² + 6)(3² + 6)(7² + 6)(13² + 6)(18² + 6) = (1² + 6)(2² + 6)(3² + 6)(8² + 6)(213² + 6)
= (1² + 6)(2² + 6)(3² + 6)(37² + 6)(48² + 6) = (1² + 6)(2² + 6)(12² + 6)(15² + 6)(37² + 6)
= (1² + 6)(3² + 6)(4² + 6)(7² + 6)(12² + 6)(13² + 6) = (1² + 6)(3² + 6)(4² + 6)(7² + 6)(162² + 6)
= (1² + 6)(3² + 6)(7² + 6)(12² + 6)(62² + 6) = (1² + 6)(3² + 6)(8² + 6)(18² + 6)(37² + 6)
= (1² + 6)(6² + 6)(7² + 6)(12² + 6)(37² + 6) = (1² + 6)(7² + 6)(12² + 6)(13² + 6)(18² + 6)
= (1² + 6)(7² + 6)(18² + 6)(162² + 6) = (1² + 6)(8² + 6)(12² + 6)(213² + 6)
= (1² + 6)(12² + 6)(37² + 6)(48² + 6) = (12² + 6)(22² + 6)(213² + 6) = (12² + 6)(29² + 6)(162² + 6)
= (2² + 6)(18² + 6)(27² + 6)(37² + 6) = (2² + 6)(3² + 6)(4² + 6)(27² + 6)(37² + 6)
= (2² + 6)(3² + 6)(7² + 6)(13² + 6)(48² + 6) = (2² + 6)(3² + 6)(8² + 6)(15² + 6)(37² + 6)
= (2² + 6)(3² + 6)(12² + 6)(13² + 6)(29² + 6) = (2² + 6)(3² + 6)(22² + 6)(213² + 6)
= (2² + 6)(3² + 6)(29² + 6)(162² + 6) = (2² + 6)(6² + 6)(13² + 6)(213² + 6)
= (2² + 6)(7² + 6)(12² + 6)(13² + 6)(15² + 6) = (2² + 6)(7² + 6)(15² + 6)(162² + 6)
= (3² + 6)(4² + 6)(6² + 6)(13² + 6)(37² + 6) = (3² + 6)(6² + 6)(7² + 6)(8² + 6)(37² + 6)
= (3² + 6)(6² + 6)(37² + 6)(62² + 6) = (3² + 6)(7² + 6)(8² + 6)(13² + 6)(18² + 6)
= (3² + 6)(8² + 6)(37² + 6)(48² + 6) = (3² + 6)(92² + 6)(162² + 6)
= (3² + 6)(12² + 6)(13² + 6)(92² + 6) = (3² + 6)(13² + 6)(18² + 6)(62² + 6)
= (3² + 6)(18² + 6)(22² + 6)(37² + 6) = (4² + 6)(12² + 6)(27² + 6)(37² + 6)
= (6² + 6)(13² + 6)(18² + 6)(37² + 6) = (7² + 6)(12² + 6)(13² + 6)(48² + 6)
= (7² + 6)(48² + 6)(162² + 6) = (8² + 6)(12² + 6)(15² + 6)(37² + 6).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57754

57754²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57756

57756² = 3335755536, 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

57758

57758²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57770

57770² = (23² + 1)(33² + 1)(76² + 1).

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

57800

57800² = (1² + 4)(4² + 4)(8² + 4)(9² + 4)(76² + 4).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57812

57812²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57816

57816² = (1² + 8)(16² + 8)(24² + 8)(49² + 8) = (5² + 8)(8² + 8)(24² + 8)(49² + 8).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57850

57850² = (1² + 4)(3² + 4)(36² + 4)(199² + 4) = (1² + 4)(4² + 4)(29² + 4)(199² + 4)
= (3² + 4)(11² + 4)(21² + 4)(68² + 4) = (1² + 9)(2² + 9)(4² + 9)(13² + 9)(76² + 9)
= (4² + 9)(11² + 9)(13² + 9)(76² + 9).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57956

57956²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57960

57960² = 716³ + 717³ + 718³ + ... + 724³.

277² + 57960 = 367², 277² - 57960 = 137².

57960² = (11² - 1)(5291² - 1) = (19² - 1)(22² - 1)(139² - 1) = (2² - 1)(11² - 1)(22² - 1)(139² - 1)
= (2² - 1)(3² - 1)(4² - 1)(22² - 1)(139² - 1) = (2² - 1)(3² - 1)(6² - 1)(22² - 1)(91² - 1)
= (2² - 1)(5² - 1)(13² - 1)(22² - 1)(24² - 1) = (22² - 1)(29² - 1)(91² - 1)
= (3² - 1)(4² - 1)(5291² - 1) = (3² - 1)(5² - 1)(8² - 1)(22² - 1)(24² - 1)
= (4² - 1)(5² - 1)(22² - 1)(139² - 1) = (5² - 1)(6² - 1)(22² - 1)(91² - 1).

Page of Squares : First Upload September 15, 2012 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57964

57964² = 2815 x 2816 + 2817 x 2818 + 2819 x 2820 + 2821 x 2822 + ... + 3487 x 3488.

Page of Squares : First Upload September 15, 2012 ; Last Revised September 15, 2012
by Yoshio Mimura, Kobe, Japan

57968

57968²± 3 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57969

57969² = (13² + 2)(4433² + 2).

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan

57987

57987²± 2 are primes.

Page of Squares : First Upload March 19, 2014 ; Last Revised March 19, 2014
by Yoshio Mimura, Kobe, Japan