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81090

81090² = (3² + 9)(6² + 9)(16² + 9)(175² + 9) = (5² + 9)(9² + 9)(16² + 9)(90² + 9)
= (5² + 9)(12² + 9)(16² + 9)(69² + 9) = (6² + 9)(69² + 9)(175² + 9).

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

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81120

338² + 81120 = 442², 338² - 81120 = 182².

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

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81172

81172² = (7² + 3)(19² + 3)(590² + 3).

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

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81180

81180²= 31 x 32 + 32 x 33 + 33 x 34 + 34 x 35 + ... + 2703 x 2704.

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

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81222

81222² = 6597013284, 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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81225

81225 = 285², and 81 = 9², 255 = 15².

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

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81243

81243² = (5² + 2)(7² + 2)(23² + 2)(95² + 2).

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

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81270

81270² = (1² + 5)(10² + 5)(34² + 5)(95² + 5) = (2² + 5)(5² + 5)(9² + 5)(10² + 5)(52² + 5)
= (2² + 5)(5² + 5)(52² + 5)(95² + 5) = (4² + 5)(5² + 5)(9² + 5)(10² + 5)(34² + 5)
= (4² + 5)(5² + 5)(34² + 5)(95² + 5) = (4² + 5)(9² + 5)(20² + 5)(95² + 5)
= (5² + 5)(9² + 5)(1600² + 5) = (9² + 5)(10² + 5)(25² + 5)(34² + 5) = (25² + 5)(34² + 5)(95² + 5).

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

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81289

81289 = 156⁴ + 195⁴ + 260⁴.

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

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81306

81306²± 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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81346

81346² = 6617171716, a square with 3 kinds of digits.

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

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81378

81378² = (1² + 2)(2² + 2)(86² + 2)(223² + 2) = (4² + 2)(86² + 2)(223² + 2).

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

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81404

81404² = 6626611216, a square with 3 kinds of digits.

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

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81500

81500²± 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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81518

81518²± 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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81534

81534²± 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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81606

81606² = (14² + 5)(71² + 5)(81² + 5).

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

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81614

81614² = (7² + 3)(56² + 3)(202² + 3).

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

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81618

81618² = (19² + 5)(21² + 5)(202² + 5).

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

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81619

81619² = 6661661161, a square with 2 kinds of digits.

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

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81620

81620² = (1² + 6)(2² + 6)(4² + 6)(10² + 6)(202² + 6) = (4² + 6)(8² + 6)(10² + 6)(202² + 6).

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

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81662

81662² = 6668682244, 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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81664

81664² = (1² + 7)(2² + 7)(5² + 7)(15² + 7)(101² + 7) = (1² + 7)(2² + 7)(13² + 7)(15² + 7)(43² + 7)
= (2² + 7)(3² + 7)(9² + 7)(15² + 7)(43² + 7) = (2² + 7)(5² + 7)(43² + 7)(101² + 7)
= (3² + 7)(13² + 7)(15² + 7)(101² + 7) = (3² + 7)(15² + 7)(31² + 7)(43² + 7)
= (5² + 7)(9² + 7)(15² + 7)(101² + 7) = (9² + 7)(13² + 7)(15² + 7)(43² + 7)
= (15² + 7)(53² + 7)(101² + 7).

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

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81702

81702²± 5 are primes.

81702² = (1² + 2)(24² + 2)(40² + 2)(49² + 2) = (5² + 2)(7² + 2)(10² + 2)(218² + 2).

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

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81732

81732²± 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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81750

81750² = (10² + 9)(79² + 9)(99² + 9).

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

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81770

81770² = (1² + 1)(6² + 1)(8² + 1)(31² + 1)(38² + 1)
= (2² + 1)(4² + 1)(6² + 1)(31² + 1)(47² + 1) = (2² + 1)(5² + 1)(6² + 1)(31² + 1)(38² + 1)
= (4² + 1)(6² + 1)(8² + 1)(13² + 1)(31² + 1) = (4² + 1)(8² + 1)(21² + 1)(117² + 1)
= (5² + 1)(6² + 1)(8² + 1)(327² + 1) = (8² + 1)(31² + 1)(327² + 1)
= (1² + 4)(3² + 4)(8² + 4)(25² + 4)(49² + 4) = (9² + 4)(12² + 4)(25² + 4)(29² + 4).

Page of Squares : First Upload November 16, 2013 ; Last Revised April 5, 2014
by Yoshio Mimura, Kobe, Japan

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81774

81774²± 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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81778

81778²± 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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81795

81795²± 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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81796

81796 = 286², 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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81813

81813² = 6693366969, a square with 3 kinds of digits.

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

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81816

81816²± 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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81900

81900² = (2² - 1)(6² - 1)(9² - 1)(14² - 1)(64² - 1).

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

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81906

81906² = (1² + 2)(3² + 2)(12² + 2)(1180² + 2) = (3² + 2)(12² + 2)(24² + 2)(85² + 2).

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

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81914

81914²± 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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81945

81945² = 6714983025, 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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81952

81952²± 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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81978

81978²± 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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