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75000

325² + 75000 = 425², 325² - 75000 = 175².

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

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75012

A cubic polynomial:
(X + 112²)X + 147²)(X + 396²) = X³ + 437²X² + 75012²X + 6519744².

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

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75033

75033²± 2 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75034

75034²± 3 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75042

75042² = (1² + 2)(2² + 2)(3² + 2)(4² + 2)(1257² + 2) = (1² + 2)(2² + 2)(14² + 2)(1257² + 2)
= (1² + 2)(4² + 2)(8² + 2)(1257² + 2) = (4² + 2)(14² + 2)(1257² + 2).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75044

75044²± 3 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75051

75051² = 659² + 660² + 661² + ... + 2580².

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

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75075

75075² = (4² - 1)(6² - 1)(12² - 1)(274² - 1) = (6² - 1)(12² - 1)(14² - 1)(76² - 1).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75078

75078² = (16² + 2)(17² + 2)(274² + 2).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75140

75140² = (1² + 1)(3² + 1)(4² + 1)(5² + 1)(21² + 1)(38² + 1)
= (1² + 1)(4² + 1)(13² + 1)(21² + 1)(47² + 1) = (1² + 1)(5² + 1)(13² + 1)(21² + 1)(38² + 1).

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

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75144

75144²± 5 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75153

75153² = 144³ + 145³ + 146³ + 147³ + ... + 389³.

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

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75174

75174² = (3² + 2)(20² + 2)(24² + 2)(47² + 2).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75240

75240² = (2² - 1)(3² - 1)(4² - 1)(11² - 1)(362² - 1) = (2² - 1)(4² - 1)(31² - 1)(362² - 1)
= (2² - 1)(21² - 1)(37² - 1)(56² - 1) = (3² - 1)(4² - 1)(19² - 1)(362² - 1)
= (4² - 1)(5² - 1)(11² - 1)(362² - 1) = (11² - 1)(19² - 1)(362² - 1).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75264

280² + 75264 = 392², 280² - 75264 = 56².

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

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75276

75276² = (1² + 8)(3² + 8)(14² + 8)(19² + 8)(22² + 8) = (2² + 8)(3² + 8)(37² + 8)(142² + 8)
= (14² + 8)(37² + 8)(142² + 8) = (142² + 8)(530² + 8).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75278

75278² = (4² + 3)(89² + 3)(194² + 3).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75294

75294² = (23² + 5)(29² + 5)(112² + 5).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75328

75328² = (2² + 7)(3² + 7)(5² + 7)(10² + 7)(97² + 7) = (5² + 7)(10² + 7)(13² + 7)(97² + 7)
= (10² + 7)(75² + 7)(97² + 7).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75336

75336² = (24² + 8)(32² + 8)(97² + 8).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75339

75339²± 2 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75372

75372² = (5² + 8)(6² + 8)(1978² + 8) = (38² + 8)(1978² + 8).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75400

75400² = (1² + 4)(2² + 4)(3² + 4)(5² + 4)(614² + 4) = (1² + 4)(2² + 4)(5² + 4)(11² + 4)(198² + 4)
= (1² + 4)(3² + 4)(4² + 4)(5² + 4)(16² + 4)(24² + 4) = (1² + 4)(3² + 4)(10² + 4)(11² + 4)(82² + 4)
= (1² + 4)(3² + 4)(82² + 4)(114² + 4) = (1² + 4)(5² + 4)(6² + 4)(29² + 4)(34² + 4)
= (1² + 4)(5² + 4)(10² + 4)(614² + 4) = (1² + 4)(14² + 4)(29² + 4)(82² + 4)
= (2² + 4)(11² + 4)(29² + 4)(82² + 4) = (3² + 4)(4² + 4)(5² + 4)(24² + 4)(36² + 4)
= (3² + 4)(5² + 4)(6² + 4)(614² + 4) = (3² + 4)(5² + 4)(10² + 4)(11² + 4)(34² + 4)
= (3² + 4)(5² + 4)(34² + 4)(114² + 4) = (3² + 4)(34² + 4)(614² + 4)
= (5² + 4)(14² + 4)(29² + 4)(34² + 4) = (5² + 4)(16² + 4)(24² + 4)(36² + 4)
= (5² + 4)(6² + 4)(11² + 4)(198² + 4) = (11² + 4)(34² + 4)(198² + 4).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75436

75436²± 3 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75444

75444²± 5 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75459

75459²± 2 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75465

75465²± 2 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75544

75544²± 3 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75546

75546²± 5 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75547

75547² = 1413² + 1415² + 1417² + 1419² + ... + 3333².

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

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75576

75576² = 5711731776, 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

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75585

75585²± 2 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75600

375² + 75600 = 465², 375² - 75600 = 255².

75600² = (2² - 1)(4² - 1)(5² - 1)(6² - 1)(8² - 1)(49² - 1)
= (2² - 1)(4² - 1)(5² - 1)(6² - 1)(15² - 1)(26² - 1) = (2² - 1)(4² - 1)(8² - 1)(29² - 1)(49² - 1)
= (2² - 1)(4² - 1)(15² - 1)(26² - 1)(29² - 1) = (2² - 1)(6² - 1)(7² - 1)(26² - 1)(41² - 1)
= (2² - 1)(6² - 1)(8² - 1)(19² - 1)(49² - 1) = (2² - 1)(6² - 1)(15² - 1)(19² - 1)(26² - 1)
= (2² - 1)(17² - 1)(26² - 1)(99² - 1) = (4² - 1)(6² - 1)(26² - 1)(127² - 1)
= (6² - 1)(7² - 1)(8² - 1)(9² - 1)(26² - 1) = (6² - 1)(7² - 1)(26² - 1)(71² - 1)
= (6² - 1)(9² - 1)(26² - 1)(55² - 1) = (6² - 1)(17² - 1)(26² - 1)(29² - 1)
= (8² - 1)(9² - 1)(26² - 1)(41² - 1) = (26² - 1)(41² - 1)(71² - 1).

Page of Squares : First Upload November 10, 2012 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75625

75625 = 275², a zigzag square.

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

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75628

75628² = (16² + 3)(17² + 3)(275² + 3).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75696

75696² = (4² + 8)(18² + 8)(848² + 8).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75726

75726²± 5 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75744

75744² = 5737153536, 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

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75756

75756²± 5 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75759

75759² = 5739426081, a square with different digits.

Page of Squares : First Upload November 10, 2012 ; Last Revised November 10, 2012
by Yoshio Mimura, Kobe, Japan

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75783

75783²± 2 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75788

75788²± 3 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75801

75801²± 2 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75832

75832²± 3 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75850

75850² = (2² + 1)(9² + 1)(32² + 1)(117² + 1) = (6² + 1)(9² + 1)(32² + 1)(43² + 1)
= (4² + 9)(14² + 9)(19² + 9)(55² + 9).

Page of Squares : First Upload November 16, 2013 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75852

75852² = (1² + 5)(3² + 5)(9² + 5)(17² + 5)(52² + 5).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75867

75867² = (5² + 8)(83² + 8)(159² + 8).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75894

75894² = (2² + 3)(6² + 3)(54² + 3)(85² + 3).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75904

75904²± 3 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75950

75950² = (1² + 6)(13² + 6)(22² + 6)(98² + 6).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75966

75966²± 5 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75974

75974²± 3 are primes.

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75978

75978² = (2² + 5)(4² + 5)(7² + 5)(14² + 5)(53² + 5) = (14² + 5)(53² + 5)(101² + 5).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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75990

75990² = (9² + 9)(17² + 9)(464² + 9).

Page of Squares : First Upload April 2, 2014 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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