Squares:36000s

36018

36018² = (2² + 5)(71² + 5)(169² + 5) = (8² + 5)(61² + 5)(71² + 5) = (13² + 5)(16² + 5)(169² + 5).

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

36024

36024²± 5 are primes.

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

36025

36025² = 1411² + 1413² + 1415² + 1417² + ... + 2195².

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36026

36026²± 3 are primes.

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

36036

36036² = 336*337*338 + 338*339*340 + 340*341*342 + 342*343*344 + ... + 388*389*390.

Page of Squares : First Upload October 26, 2103 ; Last Revised October 26, 2103
by Yoshio Mimura, Kobe, Japan

36040

36040²± 5 are primes.

36040² = (1² + 4)(4² + 4)(7² + 4)(8² + 4)(60² + 4).

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

36046

36046²± 3 are primes.

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

36066

36066²± 5 are primes.

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

36098

36098²± 3 are primes.

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

36100

36100 =190², with 36 = 6² and 100 = 10².

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36108

36108² = (2² + 8)(3² + 8)(13² + 8)(190² + 8) = (3² + 8)(13² + 8)(14² + 8)(46² + 8)
= (3² + 8)(46² + 8)(190² + 8) = (13² + 8)(14² + 8)(190² + 8).

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

36124

36124²± 3 are primes.

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

36132

36132²± 5 are primes.

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

36134

36134² = 307 x 308 + 309 x 310 + 311 x 312 + 313 x 314 + ... + 1987 x 1988.

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36156

36156² = 773² + 774² + 775² + ... + 1636².

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36162

36162² = (2² + 5)(3² + 5)(4² + 5)(703² + 5) = (2² + 5)(17² + 5)(703² + 5)
= (3² + 5)(6² + 5)(17² + 5)(88² + 5) = (3² + 5)(6² + 5)(32² + 5)(47² + 5)
= (4² + 5)(11² + 5)(703² + 5).

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

36213

36213²± 2 are primes.

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

36279

36279²± 2 are primes.

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

36288

36288² = (2² - 1)(3² - 1)(8² - 1)(17² - 1)(55² - 1) = (5² - 1)(8² - 1)(17² - 1)(55² - 1).

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

36309

36309² = (4² + 3)(6² + 3)(12² + 3)(110² + 3).

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

36312

36312² = (3² + 8)(20² + 8)(436² + 8) = (9² + 8)(48² + 8)(80² + 8).

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

36320

36320²± 3 are primes.

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

36334

36334²± 3 are primes.

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

36344

36344² = 1250 x 1251 + 1252 x 1253 + 1254 x 1255 + 1256 x 1257 + ... + 2144 x 2145.

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36361

36361² = 1322122321, a square with 3 kinds of digits 1,2,3.

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36365

36365² =1322413225.

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36366

36366²± 5 are primes.

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

36372

A cubic polynomial:
(X + 7²)(X + 108²)(X + 336²) = X³ + 353²X² + 36372²X + 254016².

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36376

36376²± 3 are primes.

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

36416

36416² = (1² + 7)(12875² + 7).

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

36432

36432² = (2² - 1)(10² - 1)(45² - 1)(47² - 1).

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

36456

36456² = (1² + 3)(2² + 3)(11² + 3)(12² + 3)(51² + 3) = (1² + 3)(2² + 3)(51² + 3)(135² + 3)
= (1² + 3)(3² + 3)(5² + 3)(12² + 3)(82² + 3) = (1² + 3)(11² + 3)(12² + 3)(135² + 3)
= (2² + 3)(3² + 3)(5² + 3)(9² + 3)(82² + 3) = (2² + 3)(9² + 3)(11² + 3)(135² + 3)
= (5² + 3)(11² + 3)(12² + 3)(51² + 3) = (5² + 3)(51² + 3)(135² + 3).

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

36464

36464² = (5² + 7)(6² + 7)(983² + 7) = (37² + 7)(983² + 7).

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

36480

36480² = (2² - 1)(3² - 1)(39² - 1)(191² - 1) = (3² - 1)(9² - 1)(37² - 1)(39² - 1)
= (5² - 1)(39² - 1)(191² - 1).

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

36481

36481 = 191², a zigzag square with different digits.

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36490

36490²± 3 are primes.

36490² = (4² + 9)(13² + 9)(547² + 9) = (13² + 9)(14² + 9)(191² + 9).

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

36504

195² + 36504 = 273², 195² - 36504 = 39².

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36540

36540² = (1² + 5)(3² + 5)(5² + 5)(10² + 5)(71² + 5) = (1² + 5)(3² + 5)(5² + 5)(16² + 5)(45² + 5)
= (1² + 5)(4² + 5)(5² + 5)(13² + 5)(45² + 5) = (1² + 5)(13² + 5)(25² + 5)(45² + 5)
= (2² + 5)(3² + 5)(5² + 5)(13² + 5)(45² + 5) = (3² + 5)(5² + 5)(25² + 5)(71² + 5)
= (4² - 1)(6² - 1)(28² - 1)(57² - 1) = (5² + 5)(11² + 5)(13² + 5)(45² + 5)
= (9² - 1)(28² - 1)(146² - 1).

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

36556

36556² = (4² + 3)(7² + 3)(1163² + 3).

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

36582

36582² = (6² + 3)(8² + 3)(12² + 3)(59² + 3).

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

36624

36624² = (1² + 3)(3² + 3)(5² + 3)(999² + 3).

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

36651

36651²± 2 are primes.

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

36667

36667² = 1344468889, a square with non-decreasing sequences of digits.

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36720

36720² = (2² - 1)(5² - 1)(16² - 1)(271² - 1) = (4² - 1)(16² - 1)(17² - 1)(35² - 1)
= (4² - 1)(35² - 1)(271² - 1).

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

36729

36729² = 265³ + 266³ + 267³ + ... + 318³.

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36740

36740² = 342 x 343 + 344 x 345 + 346 x 347 + 348 x 349 + ... + 2010 x 2011.

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36750

36750² = (1² + 6)(2² + 6)(12² + 6)(13² + 6)(27² + 6) = (1² + 6)(2² + 6)(27² + 6)(162² + 6)
= (1² + 6)(3² + 6)(12² + 6)(13² + 6)(22² + 6) = (1² + 6)(3² + 6)(22² + 6)(162² + 6)
= (1² + 6)(6² + 6)(13² + 6)(162² + 6) = (2² + 6)(3² + 6)(6² + 6)(463² + 6)
= (2² + 6)(3² + 6)(8² + 6)(13² + 6)(27² + 6) = (6² + 6)(12² + 6)(463² + 6)
= (8² + 6)(12² + 6)(13² + 6)(27² + 6) = (8² + 6)(27² + 6)(162² + 6).

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

36804

36804²± 5 are primes.

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

36810

36810² = (3² + 9)(20² + 9)(429² + 9).

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

36864

36864 = 192², a square pegged by 6.

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36882

36882²± 5 are primes.

36882² = (2² + 5)(7² + 5)(1673² + 5).

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

36903

36903²± 2 are primes.

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

36927

36927²± 2 are primes.

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

36941

36941 ² is the sum of (13x + 11)² where x runs over 0, 1,..., 288.

Page of Squares : First Upload June 23 2012 ; Last Revised June 23, 2012
by Yoshio Mimura, Kobe, Japan

36960

442² + 36960 = 482², 442² - 36960 = 398².

36960² = (2² - 1)(6² - 1)(15² - 1)(241² - 1) = (3² - 1)(6² - 1)(34² - 1)(65² - 1)
= (3² - 1)(9² - 1)(34² - 1)(43² - 1) = (6² - 1)(7² - 1)(21² - 1)(43² - 1)
= (6² - 1)(13² - 1)(21² - 1)(23² - 1) = (9² - 1)(21² - 1)(197² - 1) = (21² - 1)(41² - 1)(43² - 1).

Page of Squares : First Upload June 23 2012 ; Last Revised February 28, 2014
by Yoshio Mimura, Kobe, Japan

36964

36964²± 3 are primes.

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

36966

36966²± 5 are primes.

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

36975

36975² = (22² + 9)(36² + 9)(46² + 9).

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