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84000

565² + 84000 = 635², 565² - 84000 = 485²,
370² + 84000 = 470², 370² - 84000 = 230²,
290² + 84000 = 410², 290² - 84000 = 10².

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84004

84004²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84032

84032²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84042

84042² = (3² + 5)(8² + 5)(38² + 5)(71² + 5) = (4² + 5)(8² + 5)(31² + 5)(71² + 5)
= (8² + 5)(13² + 5)(767² + 5) = (31² + 5)(38² + 5)(71² + 5).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84056

84056² = (1² + 3)(4² + 3)(47² + 3)(205² + 3).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84057

84057²± 2 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84064

84064² = (1² + 7)(8² + 7)(17² + 7)(205² + 7).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84094

84094²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84100

84100² = (1² + 1)(2² + 1)(3² + 1)(12² + 1)(17² + 1)(41² + 1)
= (1² + 1)(7² + 1)(12² + 1)(17² + 1)(41² + 1).

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

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84132

84132² = (1² + 8)(7² + 8)(26² + 8)(142² + 8) = (2² + 8)(7² + 8)(22² + 8)(145² + 8)
= (7² + 8)(19² + 8)(22² + 8)(26² + 8) = (22² + 8)(26² + 8)(145² + 8).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84240

291² + 84240 = 411², 291² - 84240 = 21².

84240² = (2² - 1)(4² - 1)(14² - 1)(17² - 1)(53² - 1).

Page of Squares : First Upload December 1, 2012 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84294

84294² = (4² + 5)(21² + 5)(871² + 5).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84304

84304²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84354

84354² = 7115597316, 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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84357

84357²± 2 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84366

84366² = 964² + 965² + 966² + ... + 2812².

84366² = (1² + 5)(2² + 5)(9² + 5)(1238² + 5) = (7² + 5)(9² + 5)(1238² + 5).

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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84368

84368²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84378

84378² = (3² + 5)(32² + 5)(703² + 5).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84419

84419² = 1161² + 1162² + 1163² + ... + 2841².

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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84435

84435²± 2 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84441

84441²± 2 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84448

84448²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84480

488² + 84480 = 568², 488² - 84480 = 392²,
292² + 84480 = 412², 292² - 84480 = 28².

84480² = (3² - 1)(7² - 1)(9² - 1)(21² - 1)(23² - 1) = (7² - 1)(9² - 1)(21² - 1)(65² - 1).

Page of Squares : First Upload December 1, 2012 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84500

84500² = (3² + 4)(4² + 4)(11² + 4)(16² + 4)(29² + 4).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84525

84525² = (2² - 1)(6² - 1)(24² - 1)(344² - 1).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84530

84530² = (23² + 6)(28² + 6)(130² + 6).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84540

The quadratic polynomial 84540X² - 556260X + 1240849 takes the values 877², 683², 577², 607², 757², 973² at X = 1, 2,..., 6.

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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84550

84550²± 3 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84552

84552² = (1² + 3)(3² + 3)(57² + 3)(214² + 3).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84606

84606² = 899² + 900² + 901² + ... + 2810².

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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84648

84648² = 7165283904, a square with different digits.

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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84666

84666²± 5 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84672

84672² = (2² - 1)(5² - 1)(8² - 1)(13² - 1)(97² - 1) = (8² - 1)(13² - 1)(15² - 1)(55² - 1).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84680

84680²= 1266 x 1267 + 1267 x 1268 + 1268 x 1269 +...+ 2865 x 2866.

84680² = (19² + 4)(54² + 4)(82² + 4).

Page of Squares : First Upload December 1, 2012 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84700

84700² = (2² + 6)(4² + 6)(7² + 6)(8² + 6)(92² + 6) = (2² + 6)(4² + 6)(62² + 6)(92² + 6).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84730

84730² = (1² + 4)(15² + 4)(2504² + 4).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84762

84762² = 1247² + 1249² + 1251² + 1253² + ... + 3557².

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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84800

84800² = (2² + 4)(6² + 4)(7² + 4)(14² + 4)(46² + 4).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84846

84846²± 5 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84864

84864² = (25² - 1)(33² - 1)(103² - 1).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84870

84870² = (2² + 5)(6² + 5)(8² + 5)(15² + 5)(35² + 5).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84882

84882² = (1² + 5)(9² + 5)(18² + 5)(206² + 5).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84906

84906² = (3² + 9)(13² + 9)(1500² + 9).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84915

84915² = (6² + 9)(12² + 9)(18² + 9)(56² + 9).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84932

84932² = 1752² + 1753² + 1754² + ... + 3000².

Page of Squares : First Upload December 1, 2012 ; Last Revised December 1, 2012
by Yoshio Mimura, Kobe, Japan

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84970

84970² = (17² + 4)(4964² + 4).

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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84987

84987²± 2 are primes.

Page of Squares : First Upload April 5, 2014 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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