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86016

20⁴ + 86016 = 496², 20⁴ - 86016 = 272².

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

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86020

86020² = 659 x 660 + 661 x 662 + 663 x 664 + 665 x 666 + ... + 3547 x 3548.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

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86022

86022² = (1² + 2)(4² + 2)(23² + 2)(508² + 2).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86043

86043² = 2087² + 2089² + 2091² + 2093² + ... + 3767².

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

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86058

86058² = (2² + 5)(3² + 5)(4² + 5)(1673² + 5) = (2² + 5)(17² + 5)(1673² + 5)
= (4² + 5)(11² + 5)(1673² + 5).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86064

86064² = (2² + 8)(36² + 8)(688² + 8).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86073

86073² = 7408561329, a square with different digits.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

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86110

86110²= 3904 x 3905 + 3905 x 3906 + 3906 x 3907 +...+ 4339 x 4340.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

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86190

86190² = (2² + 9)(63² + 9)(379² + 9).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86206

86206²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86256

86256²± 5 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86268

86268² = (1² + 3)(12² + 3)(32² + 3)(111² + 3) = (2² + 3)(3² + 3)(6² + 3)(32² + 3)(47² + 3)
= (2² + 3)(6² + 3)(47² + 3)(111² + 3) = (2² + 3)(9² + 3)(32² + 3)(111² + 3)
= (6² + 3)(9² + 3)(32² + 3)(47² + 3).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86283

86283²± 2 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86296

86296²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86318

86318²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86388

86388²± 5 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86400

300² + 86400 = 420², 300² - 86400 = 60².

86400² = (2² - 1)(3² - 1)(4² - 1)(5² - 1)(19² - 1)(49² - 1)
= (2² - 1)(3² - 1)(7² - 1)(9² - 1)(11² - 1)(26² - 1) = (2² - 1)(4² - 1)(7² - 1)(9² - 1)(11² - 1)(19² - 1)
= (2² - 1)(5² - 1)(11² - 1)(19² - 1)(49² - 1) = (2² - 1)(7² - 1)(9² - 1)(26² - 1)(31² - 1)
= (3² - 1)(4² - 1)(5² - 1)(7² - 1)(9² - 1)(26² - 1) = (3² - 1)(4² - 1)(49² - 1)(161² - 1)
= (3² - 1)(7² - 1)(9² - 1)(19² - 1)(26² - 1) = (5² - 1)(7² - 1)(9² - 1)(11² - 1)(26² - 1)
= (11² - 1)(49² - 1)(161² - 1).

Page of Squares : First Upload December 8, 2012 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86430

86430² = (5² + 5)(9² + 5)(14² + 5)(120² + 5).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86478

86478² = 7478444484, a square with 3 kinds of digits.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

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86508

86508² = (1² + 2)(2² + 2)(4² + 2)(22² + 2)(218² + 2).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86526

86526² = 909² + 910² + 911² + ... + 2852².

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

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86530

86530² = (1² + 4)(93² + 4)(416² + 4).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86580

86580² = (1² + 9)(2² + 9)(3² + 9)(19² + 9)(93² + 9) = (1² + 9)(15² + 9)(19² + 9)(93² + 9)
= (3² + 9)(11² + 9)(19² + 9)(93² + 9).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86584

86584² = (25² + 7)(33² + 7)(104² + 7).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86598

86598² = 1303² + 1305² + 1307² + 1309² + ... + 3613².

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

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86640

323² + 86640 = 437², 323² - 86640 = 133².

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

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86670

86670² = (1² + 5)(5² + 5)(6460² + 5).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86714

86714² = 7519317796, 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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86716

86716² = (2² + 3)(4² + 3)(5² + 3)(1421² + 3) = (2² + 3)(23² + 3)(1421² + 3) = (61² + 3)(1421² + 3).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86718

86718² = (21² + 6)(24² + 6)(170² + 6).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86724

86724² = (1² + 8)(2² + 8)(49² + 8)(170² + 8) = (2² + 2)(4² + 2)(8² + 2)(12² + 2)(85² + 2)
= (10² + 8)(49² + 8)(170² + 8).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86730

86730² = (1² + 6)(3² + 6)(6² + 6)(17² + 6)(76² + 6) = (17² + 6)(42² + 6)(120² + 6)
= (27² + 6)(42² + 6)(76² + 6).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86781

86781²± 2 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86832

86832² = (4² + 8)(40² + 8)(442² + 8).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86852

86852²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86865

86865²± 2 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86928

86928²± 5 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86940

86940² = (1² + 5)(2² + 5)(3² + 5)(4² + 5)(5² + 5)(8² + 5)(15² + 5)
= (1² + 5)(2² + 5)(3² + 5)(5² + 5)(15² + 5)(38² + 5)
= (1² + 5)(2² + 5)(3² + 5)(8² + 5)(15² + 5)(25² + 5)
= (1² + 5)(2² + 5)(4² + 5)(5² + 5)(15² + 5)(31² + 5)
= (1² + 5)(2² + 5)(5² + 5)(8² + 5)(15² + 5)(17² + 5) = (1² + 5)(2² + 5)(15² + 5)(25² + 5)(31² + 5)
= (1² + 5)(3² + 5)(5² + 5)(10² + 5)(169² + 5) = (1² + 5)(3² + 5)(7² + 5)(8² + 5)(10² + 5)(15² + 5)
= (1² + 5)(3² + 5)(10² + 5)(15² + 5)(61² + 5) = (1² + 5)(3² + 5)(15² + 5)(20² + 5)(31² + 5)
= (1² + 5)(4² + 5)(5² + 5)(8² + 5)(11² + 5)(15² + 5) = (1² + 5)(5² + 5)(8² + 5)(25² + 5)(31² + 5)
= (1² + 5)(5² + 5)(11² + 5)(15² + 5)(38² + 5) = (1² + 5)(7² + 5)(10² + 5)(15² + 5)(31² + 5)
= (1² + 5)(8² + 5)(11² + 5)(15² + 5)(25² + 5) = (2² + 5)(3² + 5)(5² + 5)(8² + 5)(11² + 5)(15² + 5)
= (2² + 5)(5² + 5)(11² + 5)(15² + 5)(31² + 5) = (3² + 5)(4² + 5)(5² + 5)(7² + 5)(8² + 5)(15² + 5)
= (3² + 5)(4² + 5)(5² + 5)(15² + 5)(61² + 5) = (3² + 5)(5² + 5)(7² + 5)(15² + 5)(38² + 5)
= (3² + 5)(5² + 5)(25² + 5)(169² + 5) = (3² + 5)(7² + 5)(8² + 5)(15² + 5)(25² + 5)
= (3² + 5)(15² + 5)(25² + 5)(61² + 5) = (4² + 5)(5² + 5)(7² + 5)(15² + 5)(31² + 5)
= (5² + 5)(7² + 5)(8² + 5)(15² + 5)(17² + 5) = (5² + 5)(15² + 5)(17² + 5)(61² + 5)
= (7² + 5)(15² + 5)(25² + 5)(31² + 5).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86942

(86942² - 4) = (3² - 4)(4² - 4)(6² - 4)(9² - 4)(11² - 4)(21² - 4).

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

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86954

86954²± 3 are primes.

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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86968

86968² = 464 x 465 + 466 x 467 + 468 x 469 + 470 x 471 + ... + 3568 x 3569.

Page of Squares : First Upload December 8, 2012 ; Last Revised December 8, 2012
by Yoshio Mimura, Kobe, Japan

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86982

86982² = (4² + 3)(12² + 3)(18² + 3)(91² + 3).

Page of Squares : First Upload April 9, 2014 ; Last Revised April 9, 2014
by Yoshio Mimura, Kobe, Japan

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