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54000

54000² = (4² - 1)(11² - 1)(26² - 1)(49² - 1).

255² + 54000 = 345², 255² - 54000 = 105².

Page of Squares : First Upload September 8, 2012 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54018

54018²± 5 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54039

54039²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54075

54075² = 2924105625, and 29241 = 171², 5625 = 75².

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

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54116

54116² = (18² + 8)(2970² + 8).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54123

54123² = 2929299129 is a square with 3 kinds of digits.

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

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54144

54144²± 5 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54162

54162² = (1² + 2)(2² + 2)(23² + 2)(554² + 2) = (2² + 2)(10² + 2)(23² + 2)(95² + 2)
= (4² + 2)(23² + 2)(554² + 2).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54166

54166²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54168

54168² = (21² + 3)(27² + 3)(95² + 3).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54180

54180² = (1² + 5)(4² + 5)(5² + 5)(9² + 5)(95² + 5) = (1² + 5)(9² + 5)(25² + 5)(95² + 5)
= (2² + 5)(3² + 5)(5² + 5)(9² + 5)(95² + 5) = (5² + 5)(9² + 5)(11² + 5)(95² + 5).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54208

54208² = (1² + 7)(2² + 7)(21² + 7)(273² + 7) = (1² + 7)(7² + 7)(9² + 7)(273² + 7)
= (5² + 7)(35² + 7)(273² + 7) = (9² + 7)(21² + 7)(273² + 7).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54243

54243² = (2² + 5)(6² + 5)(32² + 5)(88² + 5).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54244

54244²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54250

54250² = (1² + 6)(2² + 6)(5² + 6)(13² + 6)(88² + 6) = (5² + 6)(8² + 6)(13² + 6)(88² + 6).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54252

54252² = (1² + 8)(2² + 8)(6² + 8)(787² + 8) = (2² + 8)(35² + 8)(446² + 8)
= (6² + 8)(10² + 8)(787² + 8).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54264

365² + 54264 = 433², 365² - 54264 = 281²,
41³ + 54280 = 351², 41³ - 54280 = 121².

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

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54289

54289 = 233² is a square with different digits.

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

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54292

54292² = (1² + 3)(2² + 3)(44² + 3)(233² + 3) = (5² + 3)(44² + 3)(233² + 3).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54335

54335² = 2952292225 is a square with 3 kinds of digits.

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

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54400

54400² = (2² + 4)(6² + 4)(8² + 4)(14² + 4)(26² + 4).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54405

54405²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54464

54464² = (3² + 7)(4² + 7)(17² + 7)(165² + 7) = (17² + 7)(19² + 7)(165² + 7).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54468

54468² = (2² + 2)(4² + 2)(24² + 2)(218² + 2) = (3² + 8)(9² + 8)(14² + 8)(98² + 8)
= (3² + 9)(5² + 9)(13² + 9)(165² + 9).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54484

54484²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54600

425² + 54600 = 485², 425² - 54600 = 355².

54600² = (2² - 1)(4² - 1)(6² - 1)(27² - 1)(51² - 1) = (3² - 1)(6² - 1)(51² - 1)(64² - 1)
= (6² - 1)(13² - 1)(14² - 1)(51² - 1) = (6² - 1)(51² - 1)(181² - 1).

Page of Squares : First Upload September 8, 2012 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54633

54633²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54652

54652²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54693

54693²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54704

54704² = 556² + 557² + 558² + ... + 2091².

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

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54720

54720² = (2² - 1)(5² - 1)(9² - 1)(721² - 1) = (3² - 1)(4² - 1)(7² - 1)(721² - 1)
= (7² - 1)(11² - 1)(721² - 1).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54730

54730² = (1² + 1)(3² + 1)(12238² + 1)
= (1² + 4)(24476² + 4) = (8² + 9)(79² + 9)(81² + 9).

Page of Squares : First Upload November 16, 2013 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54738

54738²± 5 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54741

54741²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54756

54756 = 234² is a zigzag square.

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

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54758

54758² = 2998438564, and 299843856 = 17316², 4 = 2².

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

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54772

54772²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54784

54784² = (1² + 7)(5² + 7)(10² + 7)(331² + 7) = (3² + 7)(10² + 7)(11² + 7)(117² + 7).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54810

54810² = (1² + 5)(2² + 5)(10² + 5)(16² + 5)(45² + 5) = (10² + 5)(13² + 5)(16² + 5)(25² + 5)
= (2² + 5)(4² + 5)(5² + 5)(10² + 5)(71² + 5) = (2² + 5)(4² + 5)(5² + 5)(16² + 5)(45² + 5)
= (2² + 5)(5² + 5)(45² + 5)(74² + 5) = (2² + 5)(10² + 5)(25² + 5)(71² + 5)
= (2² + 5)(16² + 5)(25² + 5)(45² + 5) = (3² + 5)(10² + 5)(20² + 5)(71² + 5)
= (3² + 5)(16² + 5)(20² + 5)(45² + 5) = (4² + 5)(5² + 5)(10² + 5)(13² + 5)(16² + 5)
= (4² + 5)(13² + 5)(20² + 5)(45² + 5) = (5² + 5)(10² + 5)(13² + 5)(74² + 5)
= (7² + 5)(10² + 5)(16² + 5)(45² + 5).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54902

54902²± 3 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54912

54912² = (3² - 1)(12² - 1)(25² - 1)(65² - 1).

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54918

54918² = 3015986724 is a square with different digits.

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

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54924

54924²± 5 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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54945

54945²± 2 are primes.

Page of Squares : First Upload March 15, 2014 ; Last Revised March 15, 2014
by Yoshio Mimura, Kobe, Japan

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