Squares:45000s

45045

45045² = (2² - 1)(4² - 1)(8² - 1)(846² - 1) = (2² - 1)(8² - 1)(12² - 1)(274² - 1)
= (2² - 1)(12² - 1)(34² - 1)(64² - 1) = (6² - 1)(10² - 1)(12² - 1)(64² - 1)
= (8² - 1)(12² - 1)(14² - 1)(34² - 1).

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

45050

45050² = (2² + 1)(4² + 1)(7² + 1)(23² + 1)(30² + 1)
= (7² + 4)(9² + 4)(11² + 4)(60² + 4) = (1² + 9)(4² + 9)(16² + 9)(175² + 9).

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

45056

45056² = (1² + 7)(2² + 7)(5² + 7)(11² + 7)(75² + 7) = (1² + 7)(3² + 7)(5² + 7)(9² + 7)(75² + 7)
= (1² + 7)(3² + 7)(5² + 7)(13² + 7)(53² + 7) = (1² + 7)(3² + 7)(53² + 7)(75² + 7)
= (2² + 7)(3² + 7)(5² + 7)(11² + 7)(53² + 7) = (2² + 7)(5² + 7)(13² + 7)(181² + 7)
= (2² + 7)(75² + 7)(181² + 7) = (3² + 7)(11² + 7)(13² + 7)(75² + 7)
= (5² + 7)(9² + 7)(11² + 7)(75² + 7) = (5² + 7)(11² + 7)(13² + 7)(53² + 7)
= (11² + 7)(53² + 7)(75² + 7).

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

45136

45136² = (1² + 3)(2² + 3)(5² + 3)(7² + 3)(11² + 3)(20² + 3)
= (1² + 3)(5² + 3)(11² + 3)(19² + 3)(20² + 3) = (1² + 3)(5² + 3)(11² + 3)(383² + 3).

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

45138

58722² + 45138² = 5485712328, a mosaic.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45144

45144² = (1² + 8)(5² + 8)(7² + 8)(12² + 8)(28² + 8) = (4² + 8)(5² + 8)(7² + 8)(12² + 8)(17² + 8)
= (5² + 8)(7² + 8)(16² + 8)(64² + 8) = (7² + 8)(12² + 8)(17² + 8)(28² + 8)
= (7² + 8)(16² + 8)(368² + 8) = (8² + 8)(64² + 8)(83² + 8) = (12² + 8)(44² + 8)(83² + 8).

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

45154

45154²± 3 are primes.

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

45156

45156²± 5 are primes.

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

45234

45234²± 5 are primes.

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

45262

45262² = 2048648644, a square with even digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45291

45291²± 2 are primes.

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

45305

45305² = (3² + 4)(9² + 4)(23² + 4)(59² + 4).

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

45318

45318² = 805² + 806² + 807² + 808² + ... + 1883².

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45360

45360² = (2² - 1)(8² - 1)(26² - 1)(127² - 1) = (3² - 1)(4² - 1)(17² - 1)(244² - 1)
= (8² - 1)(13² - 1)(17² - 1)(26² - 1) = (11² - 1)(17² - 1)(244² - 1).

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

45369

45369 = 213², a square with different digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45372

45372² = (3² + 3)(4² + 3)(14² + 3)(213² + 3) = (14² + 3)(15² + 3)(213² + 3).

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

45402

45402²± 5 are primes.

45402² = (1² + 5)(8² + 5)(18² + 5)(123² + 5).

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

45414

45414² = (2² + 5)(13² + 5)(16² + 5)(71² + 5).

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

45423

45423² = (2² + 5)(32² + 5)(472² + 5).

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

45426

45426² = (20² + 2)(26² + 2)(87² + 2).

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

45430

45430² = (4² + 6)(7² + 6)(17² + 6)(76² + 6).

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

45441

45441² = (1² + 8)(3² + 8)(5² + 8)(17² + 8)(37² + 8) = (1² + 2)(5² + 2)(7² + 2)(707² + 2)
= (1² + 2)(5² + 2)(19² + 2)(265² + 2) = (1² + 8)(5² + 8)(37² + 8)(71² + 8)
= (17² + 8)(37² + 8)(71² + 8).

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

45432

45432² = 2064066624, a square with even digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45450

45450² = (1² + 9)(6² + 9)(30² + 9)(71² + 9) = (3² + 9)(4² + 9)(30² + 9)(71² + 9)
= (21² + 9)(30² + 9)(71² + 9).

45450² = 102*103*104 + 103*104*105 + 104*105*106 + 105*106*107 + ... + 301*302*303.

Page of Squares : First Upload October 26, 2013 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

45465

45465² = (27² + 6)(1677² + 6).

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

45478

45478² = 2068248484, a square with even digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45501

45501²± 2 are primes.

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

45510

45510² = (1² + 9)(14² + 9)(18² + 9)(55² + 9).

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

45550

45550² = 1517 x 1518 + 1519 x 1520 + 1521 x 1522 + 1523 x 1524 + ... + 2515 x 2516.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45567

45567² = 2076351489, a square with different digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45570

45570² = (1² + 6)(2² + 6)(5² + 6)(27² + 6)(36² + 6) = (1² + 6)(3² + 6)(5² + 6)(22² + 6)(36² + 6)
= (1² + 6)(5² + 6)(6² + 6)(8² + 6)(57² + 6) = (1² + 6)(5² + 6)(6² + 6)(13² + 6)(36² + 6)
= (1² + 6)(6² + 6)(27² + 6)(98² + 6) = (1² + 6)(8² + 6)(36² + 6)(57² + 6)
= (3² + 6)(98² + 6)(120² + 6) = (5² + 6)(6² + 6)(22² + 6)(57² + 6)
= (5² + 6)(8² + 6)(27² + 6)(36² + 6) = (22² + 6)(36² + 6)(57² + 6).

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

45584

45584² = (2² + 7)(7² + 7)(20² + 7)(91² + 7).

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

45592

45592²± 3 are primes.

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

45624

45624² = 2081549376, a square with different digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45630

45630² = (6² + 9)(9² + 9)(717² + 9).

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

45633

45633²± 2 are primes.

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

45658

45658²± 3 are primes.

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

45668

45668²± 3 are primes.

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

45682

45682²± 3 are primes.

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

45705

45705²± 2 are primes.

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

45706

45706²± 3 are primes.

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

45793

45793² = 1778² + 1779² + 1780² + 1781² + ... + 2283².

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45796

45796 = 214², a square with different digits.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45800

45800² = (1² + 4)(6² + 4)(15² + 4)(214² + 4) = (14² + 4)(15² + 4)(214² + 4).

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

45808

45808²= 2143 x 2144 + 2144 x 2145 + 2145 x 2146 + 2146 x 2147 + ... + 2526 x 2527.

Page of Squares : First Upload August 4, 2012 ; Last Revised August 4, 2012
by Yoshio Mimura, Kobe, Japan

45813

45813²± 2 are primes.

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

45830

45830²± 3 are primes.

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

45864

45864² = (1² + 3)(2² + 3)(3² + 3)(6² + 3)(12² + 3)(33² + 3)
= (1² + 3)(6² + 3)(9² + 3)(12² + 3)(33² + 3) = (2² + 3)(3² + 3)(6² + 3)(7² + 3)(9² + 3)(12² + 3)
= (2² + 3)(3² + 3)(9² + 3)(12² + 3)(45² + 3) = (3² + 3)(5² + 3)(6² + 3)(12² + 3)(33² + 3)
= (3² + 3)(6² + 3)(9² + 3)(12² + 3)(19² + 3).

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

45900

45900² = (1² + 9)(3² + 9)(4² + 9)(5² + 9)(9² + 9)(12² + 9)
= (1² + 9)(3² + 9)(9² + 9)(12² + 9)(29² + 9) = (1² + 9)(5² + 9)(6² + 9)(9² + 9)(39² + 9)
= (1² + 9)(5² + 9)(9² + 9)(12² + 9)(21² + 9) = (3² + 9)(4² + 9)(5² + 9)(9² + 9)(39² + 9)
= (3² + 9)(5² + 9)(6² + 9)(9² + 9)(29² + 9) = (3² + 9)(9² + 9)(29² + 9)(39² + 9)
= (5² + 9)(9² + 9)(21² + 9)(39² + 9).

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

45928

45928² = (2² + 4)(16238² + 4).

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

45942

45942² = (1² + 3)(4² + 3)(6² + 3)(20² + 3)(42² + 3) = (6² + 3)(42² + 3)(175² + 3).

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

45944

45944²± 3 are primes.

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

45982

45982² = 2114344324, 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

45994

45994² = (2² + 9)(7² + 9)(1675² + 9).

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