Squares:43000s

43038

43038²± 5 are primes.

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

43065

43065² = 232³ + 233³ + 234³ + 235³ + 236³ + ... + 318³.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43098

The sum of divisors of 43098² is a cube 1729³.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43134

43134² = (12² + 3)(32² + 3)(111² + 3).

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

43170

43170²= 340 x 341 + 341 x 342 + 342 x 343 + 343 x 344 + ... + 1778 x 1779.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43176

43176²± 5 are primes.

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

43200

43200² = (2² - 1)(3² - 1)(7² - 1)(26² - 1)(49² - 1) = (2² - 1)(3² - 1)(11² - 1)(26² - 1)(31² - 1)
= (2² - 1)(4² - 1)(7² - 1)(19² - 1)(49² - 1) = (2² - 1)(4² - 1)(11² - 1)(19² - 1)(31² - 1)
= (3² - 1)(4² - 1)(5² - 1)(26² - 1)(31² - 1) = (3² - 1)(4² - 1)(9² - 1)(17² - 1)(26² - 1)
= (3² - 1)(19² - 1)(26² - 1)(31² - 1) = (5² - 1)(7² - 1)(26² - 1)(49² - 1)
= (5² - 1)(11² - 1)(26² - 1)(31² - 1) = (9² - 1)(11² - 1)(17² - 1)(26² - 1).

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

43230

43230² = (3² + 6)(4² + 6)(16² + 6)(147² + 6) = (16² + 6)(18² + 6)(147² + 6).

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

43254

43254² = (1² + 2)(2² + 2)(5² + 2)(40² + 2)(49² + 2) = (1² + 2)(5² + 2)(22² + 2)(218² + 2)
= (4² + 2)(5² + 2)(40² + 2)(49² + 2) = (22² + 2)(40² + 2)(49² + 2).

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

43273

43273² = 1122² + 1123² + 1124² + 1125² + ... + 1915².

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43290

43290² = (19² + 9)(24² + 9)(93² + 9) = (2² + 9)(6² + 9)(19² + 9)(93² + 9)
= (2² + 9)(93² + 9)(129² + 9).

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

43296

43296² = (4² + 8)(6² + 8)(22² + 8)(60² + 8).

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

43309

43309² = 216³ + 217³ + 218³ + 219³ + 220³ + ... + 313³.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43320

247² + 43320 = 323², 247² - 43320 = 133².

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43321

43321843321 = 208139².

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43362

43362² = (2² + 2)(3² + 2)(5² + 2)(12² + 2)(85² + 2) = (5² + 2)(8² + 2)(12² + 2)(85² + 2).

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

43382

43382²± 3 are primes.

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

43413

43413²± 2 are primes.

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

43428

43428²± 5 are primes.

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

43470

43470² = (1² + 5)(2² + 5)(4² + 5)(8² + 5)(10² + 5)(15² + 5)
= (1² + 5)(2² + 5)(5² + 5)(8² + 5)(130² + 5) = (1² + 5)(2² + 5)(10² + 5)(15² + 5)(38² + 5)
= (1² + 5)(5² + 5)(8² + 5)(10² + 5)(38² + 5) = (2² + 5)(4² + 5)(5² + 5)(15² + 5)(38² + 5)
= (2² + 5)(4² + 5)(8² + 5)(15² + 5)(25² + 5) = (2² + 5)(5² + 5)(7² + 5)(360² + 5)
= (2² + 5)(5² + 5)(8² + 5)(10² + 5)(31² + 5) = (2² + 5)(7² + 5)(15² + 5)(130² + 5)
= (2² + 5)(8² + 5)(10² + 5)(11² + 5)(15² + 5) = (2² + 5)(8² + 5)(15² + 5)(115² + 5)
= (2² + 5)(15² + 5)(25² + 5)(38² + 5) = (3² + 5)(4² + 5)(8² + 5)(15² + 5)(20² + 5)
= (3² + 5)(15² + 5)(20² + 5)(38² + 5) = (4² + 5)(5² + 5)(10² + 5)(169² + 5)
= (4² + 5)(7² + 5)(8² + 5)(10² + 5)(15² + 5) = (4² + 5)(10² + 5)(15² + 5)(61² + 5)
= (4² + 5)(15² + 5)(20² + 5)(31² + 5) = (5² + 5)(7² + 5)(8² + 5)(130² + 5)
= (5² + 5)(8² + 5)(25² + 5)(38² + 5) = (5² + 5)(61² + 5)(130² + 5)
= (7² + 5)(10² + 5)(15² + 5)(38² + 5) = (8² + 5)(15² + 5)(17² + 5)(20² + 5)
= (10² + 5)(25² + 5)(169² + 5).

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

43484

43484²± 3 are primes.

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

43512

43512² = (1² + 3)(5² + 3)(12² + 3)(16² + 3)(21² + 3) = (2² + 3)(5² + 3)(9² + 3)(16² + 3)(21² + 3)
= (3² + 3)(16² + 3)(21² + 3)(37² + 3).

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

43533

43533²± 2 are primes.

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

43630

43630²± 3 are primes.

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

43646

43646²± 3 are primes.

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

43650

43650² = (1² + 9)(6² + 9)(31² + 9)(66² + 9) = (3² + 9)(4² + 9)(31² + 9)(66² + 9)
= (21² + 9)(31² + 9)(66² + 9).

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

43680

394² + 43680 = 446², 394² - 43680 = 334²,
233² + 43680 = 313², 233² - 43680 = 103²,
218² + 43680 = 302², 218² - 43680 = 62².

43680² = (3² - 1)(4² - 1)(6² - 1)(25² - 1)(27² - 1) = (3² - 1)(6² - 1)(7² - 1)(14² - 1)(27² - 1)
= (3² - 1)(9² - 1)(27² - 1)(64² - 1) = (3² - 1)(14² - 1)(27² - 1)(41² - 1)
= (6² - 1)(11² - 1)(25² - 1)(27² - 1) = (9² - 1)(13² - 1)(14² - 1)(27² - 1)
= (9² - 1)(27² - 1)(181² - 1) = (14² - 1)(15² - 1)(209² - 1).

Page of Squares : First Upload July 28, 2012 ; Last Revised March 8, 2014
by Yoshio Mimura, Kobe, Japan

43681

43681 = 209², a square with different digits.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43696

43696²= 2602 x 2603 + 2603 x 2604 + 2604 x 2605 + 2605 x 2606 + ... + 2857 x 2858.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43708

43708² = (1² + 3)(37² + 3)(590² + 3).

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

43760

43760²± 3 are primes.

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

43768

43768²± 3 are primes.

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

43773

43773²± 2 are primes.

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

43744

43744² = 1913537536, 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

43795

43795² = 1256² + 1257² + 1258² + 1259² + ... + 1977².

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43810

43810² = (3² + 4)(41² + 4)(296² + 4).

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

43812

43812²± 5 are primes.

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

43824

43824² = (16² + 8)(18² + 8)(148² + 8).

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

43848

43848² = (28² - 1)(1567² - 1).

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

43875

43875² = (4² + 9)(6² + 9)(24² + 9)(54² + 9).

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

43902

43902² = 1927385604, a square with different digits.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43923

43923² = 1929229929, a square with 3 kinds of digits.

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43940

43940² = (1² + 1)(3² + 1)(5² + 1)(8² + 1)(239² + 1).

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

43965

43965²± 2 are primes.

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

43993

43993² = 117² + 118² + 119² + 120² + ... + 1797².

Page of Squares : First Upload July 28, 2012 ; Last Revised July 28, 2012
by Yoshio Mimura, Kobe, Japan

43995

43995²± 2 are primes.

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