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79008

79008² = 6242264064, a square with even digits.

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79068

79068² = 2927² + 2928² + 2929² + ... + 3525².

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79078

79078²± 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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79092

79092²± 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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79100

79100²± 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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79134

79134²± 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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79162

79162² = 6266622244, a square with 3 kinds of even digits.

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79200

79200² = (2² - 1)(3² - 1)(4² - 1)(21² - 1)(199² - 1) = (2² - 1)(4² - 1)(49² - 1)(241² - 1)
= (2² - 1)(11² - 1)(21² - 1)(199² - 1) = (4² - 1)(5² - 1)(21² - 1)(199² - 1)
= (4² - 1)(9² - 1)(10² - 1)(11² - 1)(21² - 1) = (4² - 1)(9² - 1)(21² - 1)(109² - 1)
= (4² - 1)(11² - 1)(21² - 1)(89² - 1) = (19² - 1)(21² - 1)(199² - 1).

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

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79206

79206² = (2² + 5)(9² + 5)(2847² + 5).

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

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79211

79211² = (63² + 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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79248

79248² = (1² + 3)(3² + 3)(39² + 3)(293² + 3).

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

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79262

79262² = 6282464644, a square with even digits.

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79300

79300² = (3² + 4)(16² + 4)(1364² + 4).

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

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79310

79310² = (4² + 6)(7² + 6)(32² + 6)(71² + 6) = (4² + 6)(71² + 6)(238² + 6).

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

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79380

79380² = (1² + 5)(2² + 5)(3² + 5)(4² + 5)(5² + 5)(10² + 5)(11² + 5)
= (1² + 5)(2² + 5)(3² + 5)(4² + 5)(5² + 5)(115² + 5)
= (1² + 5)(2² + 5)(3² + 5)(10² + 5)(11² + 5)(25² + 5) = (1² + 5)(2² + 5)(3² + 5)(25² + 5)(115² + 5)
= (1² + 5)(2² + 5)(4² + 5)(5² + 5)(17² + 5)(25² + 5)
= (1² + 5)(2² + 5)(5² + 5)(10² + 5)(11² + 5)(17² + 5) = (1² + 5)(2² + 5)(5² + 5)(17² + 5)(115² + 5)
= (1² + 5)(3² + 5)(4² + 5)(5² + 5)(17² + 5)(20² + 5)
= (1² + 5)(3² + 5)(4² + 5)(7² + 5)(10² + 5)(25² + 5) = (1² + 5)(3² + 5)(7² + 5)(10² + 5)(115² + 5)
= (1² + 5)(3² + 5)(17² + 5)(20² + 5)(25² + 5) = (1² + 5)(4² + 5)(5² + 5)(7² + 5)(10² + 5)(17² + 5)
= (1² + 5)(4² + 5)(5² + 5)(11² + 5)(115² + 5) = (1² + 5)(5² + 5)(7² + 5)(25² + 5)(32² + 5)
= (1² + 5)(7² + 5)(10² + 5)(17² + 5)(25² + 5) = (1² + 5)(11² + 5)(25² + 5)(115² + 5)
= (2² + 5)(3² + 5)(4² + 5)(5² + 5)(11² + 5)(25² + 5)
= (2² + 5)(3² + 5)(5² + 5)(7² + 5)(10² + 5)(17² + 5) = (2² + 5)(3² + 5)(5² + 5)(11² + 5)(115² + 5)
= (2² + 5)(5² + 5)(11² + 5)(17² + 5)(25² + 5) = (3² + 5)(4² + 5)(5² + 5)(7² + 5)(10² + 5)(11² + 5)
= (3² + 5)(4² + 5)(5² + 5)(7² + 5)(115² + 5) = (3² + 5)(5² + 5)(11² + 5)(17² + 5)(20² + 5)
= (3² + 5)(7² + 5)(10² + 5)(11² + 5)(25² + 5) = (3² + 5)(7² + 5)(25² + 5)(115² + 5)
= (4² + 5)(5² + 5)(7² + 5)(17² + 5)(25² + 5) = (5² + 5)(7² + 5)(10² + 5)(11² + 5)(17² + 5)
= (5² + 5)(7² + 5)(17² + 5)(115² + 5) = (6² - 1)(7² - 1)(8² - 1)(244² - 1)
= (6² - 1)(55² - 1)(244² - 1) = (8² - 1)(41² - 1)(244² - 1).

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

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79394

79394²± 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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79418

79418² = 2! + 2! + 6! + 6! + 9! + 11! + 11! + 13!.

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79427

The sum of consecutive primes 2 + 3 + 5 + 7 + 11 + ... + 79427 is a square, 17098².

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79449

79449²± 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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79458

79458² = (11² + 2)(24² + 2)(298² + 2).

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

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79464

925² + 79464 = 967², 925² - 79464 = 881².

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79516

79516²± 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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79524

79524 = 282², a square with different digits.

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79534

79534² = 2359² + 2361² + 2363² + 2365² + ... + 3709².

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79544

79544²± 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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79560

79560² = (2² - 1)(4² - 1)(35² - 1)(339² - 1).

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

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79596

79596² = (1² + 8)(10² + 8)(27² + 8)(94² + 8) = (2² + 2)(4² + 2)(8² + 2)(20² + 2)(47² + 2)
= (2² + 2)(4² + 2)(20² + 2)(382² + 2) = (6² + 8)(27² + 8)(442² + 8).

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

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79632

A cubic polynomial:
(X + 64²)(X + 171²)(X + 432²) = X³ + 469²X² + 79632²X + 4727808².

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79641

The quadratic polynomial 79641X² - 538734X + 1089529 takes the values 794², 575², 436², 457², 622², 851² at X = 1, 2,..., 6.

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79653

79653²± 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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79690

79690² = 6350496100, and 63504 = 252², 96100 = 310².

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79716

79716² = 2269² + 2270² + 2271² + ... + 3132².

79716² = (6² + 3)(17² + 3)(747² + 3).

Page of Squares : First Upload November 24, 2012 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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79764

85³ + 79764 = 833², 85³ - 79764 = 731².

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79767

79767²± 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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79792

79792²± 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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79806

79806²± 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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79808

79808²± 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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79816

79816² = (1² + 7)(30² + 7)(937² + 7).

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

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79827

79767²± 2 are primes.

79827² = 2463² + 2465² + 2467² + 2469² + ... + 3759².

Page of Squares : First Upload November 24, 2012 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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79860

79860² = 8849 x 8850 + 8851 x 8852 + 8853 x 8854 + 8855 x 8856 + ... + 9007 x 9008.

Page of Squares : First Upload November 24, 2012 ; Last Revised November 24, 2012
by Yoshio Mimura, Kobe, Japan

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79869

79869²± 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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79914

79914²± 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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79948

79948² = (2² + 7)(4² + 7)(19² + 7)(262² + 7).

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

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79950

79950² = (2² + 9)(4² + 9)(11² + 9)(14² + 9)(27² + 9) = (4² + 9)(14² + 9)(27² + 9)(41² + 9).

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

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