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78020

78020² = 380 x 381 + 381 x 382 + 382 x 383 + ... + 2635 x 2636.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78030

78030² = (5² + 9)(9² + 9)(12² + 9)(114² + 9).

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

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78051

78051²± 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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78066

78066²± 5 are primes.

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

---

78072

78072² = 6095237184, a square with different digits.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78112

78112²± 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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78120

78120² = (2² - 1)(6² - 1)(61² - 1)(125² - 1).

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

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78155

78155² = 232³ + 233³ + 234³ + 235³ + ... + 406³.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78190

78190²± 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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78196

78196² = 6114614416, a square with 3 kinds of digits.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78204

78204²± 5 are primes.

78204² = (2² + 3)(4² + 3)(9² + 3)(12² + 3)(61² + 3) = (2² + 3)(4² + 3)(12² + 3)(15² + 3)(37² + 3).

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

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78232

78232² = (2² + 7)(7² + 7)(9² + 7)(336² + 7) = (7² + 7)(31² + 7)(336² + 7).

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

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78246

78246² = (1² + 5)(2² + 5)(4² + 5)(7² + 5)(8² + 5)(38² + 5)
= (1² + 5)(2² + 5)(4² + 5)(38² + 5)(61² + 5) = (1² + 5)(8² + 5)(38² + 5)(101² + 5)
= (2² + 5)(4² + 5)(8² + 5)(11² + 5)(61² + 5) = (2² + 5)(7² + 5)(8² + 5)(11² + 5)(38² + 5)
= (2² + 5)(8² + 5)(31² + 5)(101² + 5) = (2² + 5)(11² + 5)(38² + 5)(61² + 5)
= (4² + 5)(7² + 5)(38² + 5)(61² + 5) = (4² + 5)(101² + 5)(169² + 5).

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

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78296

78296²± 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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78300

78300² = (1² + 9)(3² + 9)(4² + 9)(9² + 9)(123² + 9) = (1² + 9)(3² + 9)(7² + 9)(21² + 9)(36² + 9)
= (1² + 9)(6² + 9)(7² + 9)(9² + 9)(51² + 9) = (1² + 9)(9² + 9)(21² + 9)(123² + 9)
= (3² + 9)(4² + 9)(7² + 9)(9² + 9)(51² + 9) = (7² + 9)(9² + 9)(21² + 9)(51² + 9).

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

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78336

580² + 78336 = 644², 580² - 78336 = 508².

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78370

78370² = (1² + 4)(96² + 4)(365² + 4).

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

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78387

78387²± 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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78400

78400² = (6² - 1)(9² - 1)(15² - 1)(99² - 1).

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

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78404

78404²± 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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78408

78408² = (1² + 8)(5² + 8)(16² + 8)(280² + 8) = (16² + 8)(17² + 8)(280² + 8).

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

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78416

78416² = (2² + 4)(3² + 4)(5² + 4)(10² + 4)(140² + 4) = (2² + 4)(140² + 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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78423

78423²± 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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78429

78429²± 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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78440

78440² = (7² + 4)(46² + 4)(234² + 4).

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

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78444

78444²± 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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78453

78453² = 6154873209, a square with different digits.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78472

78472² = (48² + 8)(1632² + 8).

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

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78498

78498² = (1² + 5)(2² + 5)(32² + 5)(333² + 5) = (2² + 5)(3² + 5)(4² + 5)(23² + 5)(66² + 5)
= (2² + 5)(4² + 5)(17² + 5)(333² + 5) = (2² + 5)(17² + 5)(23² + 5)(66² + 5)
= (4² + 5)(11² + 5)(23² + 5)(66² + 5) = (7² + 5)(32² + 5)(333² + 5).

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

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78504

78504²± 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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78540

78540² = (4² - 1)(120² - 1)(169² - 1) = (6² - 1)(7² - 1)(16² - 1)(120² - 1)
= (16² - 1)(41² - 1)(120² - 1) = (34² - 1)(2311² - 1).

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

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78541

78541² = 6168688681, a square with 3 kinds of digits.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78582

78582²± 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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78624

730² + 78624 = 782², 730² - 78624 = 674²,
510² + 78624 = 582², 510² - 78624 = 426².

78624² = (2² - 1)(8² - 1)(17² - 1)(337² - 1) = (7² - 1)(8² - 1)(27² - 1)(53² - 1)
= (27² - 1)(53² - 1)(55² - 1).

Page of Squares : First Upload November 17, 2012 ; Last Revised April 2, 2014
by Yoshio Mimura, Kobe, Japan

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78636

78636²± 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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78652

53³ + 78652 = 477², 53³ - 78652 = 265².

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78657

78657²± 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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78662

78662²± 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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78702

78702²± 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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78745

The quadratic polynomial 78745X² - 232380X + 564516 takes the values 641², 644², 759², 946², 1171², 1416² at X = 1, 2,..., 6.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78752

78752² = (10² + 7)(65² + 7)(117² + 7).

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

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78792

78792² = (1² + 3)(5² + 3)(8² + 3)(12² + 3)(75² + 3) = (2² + 3)(5² + 3)(8² + 3)(9² + 3)(75² + 3)
= (3² + 3)(8² + 3)(37² + 3)(75² + 3).

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

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78800

78800² = (1² + 4)(2² + 4)(4² + 4)(2786² + 4) = (4² + 4)(6² + 4)(2786² + 4).

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

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78840

78840²= 9191 x 9192 + 9192 x 9193 + 9193 x 9194 +...+ 9263 x 9264.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78843

78843²± 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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78847

78847² = 611² + 613² + 615² + 617² + ... + 3347².

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78848

78848²± 3 are primes.

78848² = (1² + 7)(2² + 7)(3² + 7)(7² + 7)(13² + 7)(21² + 7)
= (1² + 7)(2² + 7)(5² + 7)(7² + 7)(9² + 7)(21² + 7) = (1² + 7)(2² + 7)(7² + 7)(21² + 7)(53² + 7)
= (1² + 7)(2² + 7)(11² + 7)(21² + 7)(35² + 7) = (1² + 7)(3² + 7)(9² + 7)(21² + 7)(35² + 7)
= (1² + 7)(5² + 7)(7² + 7)(21² + 7)(31² + 7) = (1² + 7)(7² + 7)(9² + 7)(11² + 7)(35² + 7)
= (2² + 7)(7² + 7)(11² + 7)(13² + 7)(21² + 7) = (3² + 7)(5² + 7)(7² + 7)(13² + 7)(35² + 7)
= (3² + 7)(7² + 7)(9² + 7)(13² + 7)(21² + 7) = (3² + 7)(7² + 7)(35² + 7)(75² + 7)
= (5² + 7)(7² + 7)(35² + 7)(53² + 7) = (7² + 7)(9² + 7)(21² + 7)(53² + 7)
= (9² + 7)(11² + 7)(21² + 7)(35² + 7).

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

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78866

78866²± 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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78880

78880² = (2² + 4)(4² + 4)(8² + 4)(9² + 4)(82² + 4) = (2² + 4)(4² + 4)(76² + 4)(82² + 4)
= (2² + 4)(5² + 4)(8² + 4)(24² + 4)(26² + 4) = (4² + 4)(8² + 4)(26² + 4)(82² + 4).

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

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78881

78881² = 6222212161, a square with 3 kinds of digits.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78897

78897²± 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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78910

78910²± 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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78912

78912² = 4! + 5! + 6! + 6! + 6! + 8! + 8! + 13!.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78922

78922² = 6228682084, a square with even digits.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78936

78936² = (2² - 1)(45² - 1)(1013² - 1).

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

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78948

78948² = (1² + 2)(2² + 2)(4² + 2)(10² + 2)(16² + 2)(27² + 2)
= (1² + 8)(3² + 8)(10² + 8)(11² + 8)(54² + 8) = (1² + 8)(3² + 8)(54² + 8)(118² + 8)
] = (2² + 8)(11² + 8)(37² + 8)(54² + 8) = (3² + 8)(11² + 8)(14² + 8)(118² + 8).

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

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78960

78960² = 8! + 9! + 10! + 10! + 13!,
78960² = 8! + 9! + 10! + 10! + 13!.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78961

78961 = 281², a square with different digits.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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78970

78970²± 3 are primes.

78970² = (16² + 9)(17² + 9)(281² + 9).

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

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78998

78998² = 6240684004, a square with even digits.

Page of Squares : First Upload November 17, 2012 ; Last Revised November 17, 2012
by Yoshio Mimura, Kobe, Japan

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