Squares:48000s

48000

260² + 48000 = 340², 260² - 48000 = 140².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48035

48035² = 2307361225, and 2307361 = 1519², 225 = 15².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48038

48038²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48048

48048² = (2² - 1)(12² - 1)(15² - 1)(155² - 1) = (10² - 1)(12² - 1)(15² - 1)(27² - 1).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48050

48050² = (5² + 6)(88² + 6)(98² + 6).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48060

48060² = (1² + 5)(5² + 5)(23² + 5)(155² + 5).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48065

The sum of (26x + 17)² is 1193637², where 0 < 26x + 17 <= 48065.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48081

48081²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48082

48082²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48090

48090² = 81*82*83 + 82*83*84 + 83*84*85 + 84*85*86 + ... + 309*310*311.

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

48100

48100² = (1² + 1)(2² + 1)(3² + 1)(5² + 1)(8² + 1)(117² + 1) = (1² + 1)(3² + 1)(5² + 1)(18² + 1)(117² + 1)
= (1² + 1)(3² + 1)(5² + 1)(31² + 1)(68² + 1) = (1² + 1)(3² + 1)(5² + 1)(6² + 1)(8² + 1)(43² + 1)
= (1² + 1)(3² + 1)(6² + 1)(31² + 1)(57² + 1) = (1² + 1)(3² + 1)(6² + 1)(7² + 1)(8² + 1)(31² + 1)
= (1² + 1)(3² + 1)(8² + 1)(31² + 1)(43² + 1) = (1² + 1)(5² + 1)(57² + 1)(117² + 1)
= (1² + 1)(5² + 1)(7² + 1)(8² + 1)(117² + 1) = (2² + 1)(3² + 1)(5² + 1)(31² + 1)(43² + 1)
= (2² + 1)(3² + 1)(5² + 1)(6² + 1)(7² + 1)(31² + 1) = (5² + 1)(7² + 1)(31² + 1)(43² + 1)
= (1² + 4)(12² + 4)(36² + 4)(49² + 4) = (12² + 4)(29² + 4)(136² + 4).

Page of Squares : First Upload November 9, 2013 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48102

48102²± 5 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48136

48136²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48207

48207²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48212

48212²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48224

48224² = (1² + 7)(33² + 7)(515² + 7).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48231

48231²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48246

48246² = (1² + 2)(10² + 2)(27² + 2)(102² + 2) = (2² + 2)(7² + 2)(27² + 2)(102² + 2).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48267

48267²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48268

48268² = 216 x 217 + 218 x 219 + 220 x 221 + 222 x 223 + 224 x 225 + ... + 2408 x 2409.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48285

48285² = (18² + 9)(2646² + 9).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48292

48292²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48300

48300² = (2² - 1)(6² - 1)(9² - 1)(22² - 1)(24² - 1).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48342

48342²± 5 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48384

300² + 48384 = 372², 300² - 48384 = 204².

48384² = (2² - 1)(3² - 1)(5² - 1)(8² - 1)(15² - 1)(17² - 1) = (2² - 1)(5² - 1)(7² - 1)(15² - 1)(55² - 1)
= (2² - 1)(13² - 1)(17² - 1)(127² - 1) = (3² - 1)(8² - 1)(17² - 1)(127² - 1) = (7² - 1)(55² - 1)(127² - 1).

Page of Squares : First Upload August 18, 2012 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48391

48391² = (82² + 3)(590² + 3).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48396

48396² = (18² + 3)(21² + 3)(127² + 3).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48412

48412² = (1² + 3)(2² + 3)(4² + 3)(19² + 3)(110² + 3) = (2² + 3)(4² + 3)(5² + 3)(7² + 3)(110² + 3)
= (2² + 3)(7² + 3)(23² + 3)(110² + 3) = (4² + 3)(5² + 3)(19² + 3)(110² + 3)
= (7² + 3)(61² + 3)(110² + 3) = (19² + 3)(23² + 3)(110² + 3) = (37² + 3)(1307² + 3).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48418

48418²= 228 x 229 + 229 x 230 + 230 x 231 + 232 x 233 + ... + 1916 x 1917.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48435

48435²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48440

48440²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48447

48447² = (2² + 5)(4² + 5)(3524² + 5).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48502

48502²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48510

48510² = (1² + 6)(3² + 6)(6² + 6)(15² + 6)(48² + 6) = (3² + 6)(4² + 6)(6² + 6)(15² + 6)(27² + 6)
= (6² + 6)(15² + 6)(18² + 6)(27² + 6).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48543

48543²± 2 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48553

48553² = (4² + 7)(10124² + 7).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48576

530² + 48576 = 574², 530² - 48576 = 482².

48576² = (23² - 1)(45² - 1)(47² - 1).

Page of Squares : First Upload August 18, 2012 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48600

15⁴ + 48600 = 315², 15⁴ - 48600 = 45².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48604

48604² = 694² + 695² + 696² + 697² + ... + 1950².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48664

48664² = (7² + 7)(6503² + 7).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48670

48670² = 1281² + 1283² + 1285² + 1287² + 1289² + ... + 2535².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48678

48678² = (2² + 3)(3² + 3)(34² + 3)(156² + 3) = (2² + 3)(4² + 3)(27² + 3)(156² + 3)
= (4² + 3)(12² + 3)(27² + 3)(34² + 3) = (9² + 3)(34² + 3)(156² + 3).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48700

48700²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48708

48708²± 5 are primes.

48708² = (1² + 2)(2² + 2)(4² + 2)(8² + 2)(11² + 2)(30² + 2)
= (2² + 2)(4² + 2)(8² + 2)(11² + 2)(52² + 2)
= (2² + 2)(4² + 2)(11² + 2)(14² + 2)(30² + 2) = (1² + 8)(5² + 8)(6² + 8)(19² + 8)(22² + 8)
= (1² + 8)(6² + 8)(17² + 8)(142² + 8) = (1² + 8)(19² + 8)(22² + 8)(38² + 8)
= (2² + 8)(5² + 8)(17² + 8)(142² + 8) = (6² + 8)(17² + 8)(19² + 8)(22² + 8).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48716

48716²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48720

48720² = (2² - 1)(3² - 1)(6² - 1)(1681² - 1) = (5² - 1)(6² - 1)(1681² - 1) = (29² - 1)(1681² - 1).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48732

48732²± 5 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48750

48750² = (1² + 9)(2² + 9)(54² + 9)(79² + 9) = (2² + 9)(79² + 9)(171² + 9)
= (11² + 9)(54² + 9)(79² + 9).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48762

48762² = (1² + 5)(2² + 5)(3² + 5)(34² + 5)(52² + 5) = (1² + 5)(11² + 5)(34² + 5)(52² + 5)
= (2² + 5)(4² + 5)(7² + 5)(9² + 5)(52² + 5) = (2² + 5)(4² + 5)(9² + 5)(11² + 5)(34² + 5)
= (3² + 5)(7² + 5)(34² + 5)(52² + 5) = (9² + 5)(52² + 5)(101² + 5).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48776

48776² = (1² + 3)(2² + 3)(8² + 3)(19² + 3)(59² + 3) = (2² + 3)(5² + 3)(7² + 3)(8² + 3)(59² + 3)
= (5² + 3)(8² + 3)(19² + 3)(59² + 3).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48794

48794²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48840

48840² = 533² + 534² + 535² + 536² + ... + 1940².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48841

48841 = 221², a sqaure with 3 kinds of digits.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48848

48848² = (3² + 7)(6² + 7)(8² + 7)(221² + 7).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48852

48852² = 2386517904, a square with different digits.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48880

48880²± 3 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48895

48895² = (7² + 6)(6593² + 6).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48918

48918²± 5 are primes.

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48951

48951² = 2396200401, 2601 = 51², 324 = 18², 900 = 30².

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48960

48960² = (2² - 1)(3² - 1)(4² - 1)(5² - 1)(16² - 1)(33² - 1) = (2² - 1)(3² - 1)(16² - 1)(19² - 1)(33² - 1)
= (2² - 1)(5² - 1)(11² - 1)(16² - 1)(33² - 1) = (2² - 1)(49² - 1)(577² - 1)
= (3² - 1)(5² - 1)(35² - 1)(101² - 1) = (3² - 1)(16² - 1)(31² - 1)(35² - 1)
= (4² - 1)(11² - 1)(33² - 1)(35² - 1) = (5² - 1)(16² - 1)(19² - 1)(33² - 1).

Page of Squares : First Upload March 12, 2014 ; Last Revised March 12, 2014
by Yoshio Mimura, Kobe, Japan

48981

1² + 2² + 3² + 4² + ... + 48981² = 39171931597391, the unique 14-digit sum which consists of odd digits .

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan

48998

48998² = 2400804004, a square with even digits.

Page of Squares : First Upload August 18, 2012 ; Last Revised August 18, 2012
by Yoshio Mimura, Kobe, Japan