Squares:28000s

28044

28044² = (7² + 8)(26² + 8)(142² + 8).

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

28072

28072² = (1² + 7)(9² + 7)(1058² + 7).

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

28080

28080² = (2² - 1)(25² - 1)(649² - 1) = (2² - 1)(4² - 1)(53² - 1)(79² - 1).

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

28089

28089²± 2 are primes.

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

28106

28106² = 454² + 455² + 456² + 457² + ... + 1350².

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28122

28122² = (1² + 5)(9² + 5)(1238² + 5).

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

28130

28130² = (1² + 1)(12² + 1)(22² + 1)(75² + 1) = (17² + 1)(22² + 1)(75² + 1)
= (1² + 4)(5² + 4)(44² + 4)(53² + 4).

Page of Squares : First Upload November 9, 2013 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

28167

28167² = 1081² + 1082² + 1083² + ... + 1538².

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28171

28171² = 793605241 is a square with different digits.

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28224

28224 = 168² is a square with even digits.

28224² = (3² - 1)(8² - 1)(13² - 1)(97² - 1).

Page of Squares : First Upload April 28, 2012 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

28236

28236² = (3² + 3)(84² + 3)(97² + 3) = (45² + 3)(627² + 3) = (6² + 3)(7² + 3)(627² + 3).

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

28256

28256² = 798401536 is a square with different digits.

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28260

28260² = 995² + 997² + 999² + 1001² + ... + 1793².

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28262

28262²± 3 are primes.

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

28275

28275²± 2 are primes.

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

28288

28288²± 3 are primes.

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

28290

28290² = (6² + 5)(8² + 5)(15² + 5)(35² + 5).

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

28293

28293²± 2 are primes.

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

28336

28336² = (19² + 7)(35² + 7)(42² + 7) = (2² + 7)(4² + 7)(5² + 7)(7² + 7)(42² + 7)
= (2² + 7)(42² + 7)(203² + 7) = (2² + 7)(7² + 7)(27² + 7)(42² + 7)
= (3² + 7)(4² + 7)(35² + 7)(42² + 7) = (5² + 7)(42² + 7)(119² + 7).

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

28340

28340²± 3 are primes.

28340² = (4² + 4)(16² + 4)(393² + 4).

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

28346

28346² = 803495716 is a square with different digits.

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28350

28350² = (5² + 5)(10² + 5)(20² + 5)(25² + 5).

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

28371

28371² = (12² + 3)(2340² + 3).

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

28378

28378²± 3 are primes.

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

28380

28380² = (8³ + 4)(116³ + 4).

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

28384

28384² = 475² + 476² + 477² + ... + 1361².

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28386

28386² = (1² + 2)(4² + 2)(9² + 2)(424² + 2).

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

28392

28392²± 5 are primes.

28392² = (1³ + 2³ + 3³ + ... + 13³)(14³ + 15³ + 16³ + ... + 25³).

28392² = (1² + 3)(2² + 3)(6² + 3)(19² + 3)(45² + 3) = (1² + 3)(3² + 3)(33² + 3)(124² + 3)
= (1² + 3)(3² + 3)(5² + 3)(6² + 3)(124² + 3) = (19² + 3)(33² + 3)(45² + 3)
= (2² + 3)(5² + 3)(6² + 3)(7² + 3)(45² + 3) = (2² + 3)(7² + 3)(33² + 3)(45² + 3)
= (3² + 3)(7² + 3)(9² + 3)(124² + 3) = (5² + 3)(6² + 3)(19² + 3)(45² + 3)
= (6² + 3)(7² + 3)(19² + 3)(33² + 3).

Page of Squares : First Upload February 9, 2013 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

28398

28398² = 806446404 is a square with even digits.

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28406

28406²± 3 are primes.

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

28448

28448² = (1² + 7)(3² + 7)(7² + 7)(336² + 7) = (3² + 7)(21² + 7)(336² + 7)
= (7² + 7)(11² + 7)(336² + 7).

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

28454

28454²± 3 are primes.

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

28470

28470² = (2² + 9)(8² + 9)(11² + 9)(81² + 9) = (8² + 9)(41² + 9)(81² + 9) = (9² + 9)(3001² + 9).

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

28479

The quadratic polynomial -28479X² + 300300X - 263900 takes the values 89², 472², 617², 694², 725², 716² at X = 1, 2,..., 6,

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28491

28491²± 2 are primes.

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

28497

A cubic polynomial:
(X + 756²)(X + 4048²)(X + 28497²) = X³ + 28793²X² + 117390252²X + 87209027136².

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28500

28500² = 812250000, and 81 = 9², 2250000 = 1500².

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28512

28512² = (1² + 8)(4² + 8)(6² + 8)(10² + 8)(28² + 8) = (1² + 8)(6² + 8)(8² + 8)(10² + 8)(16² + 8)
= (2² + 8)(4² + 8)(38² + 8)(44² + 8) = (2² + 8)(4² + 8)(5² + 8)(10² + 8)(28² + 8)
= (2² + 8)(4² + 8)(5² + 8)(6² + 8)(44² + 8) = (2² + 8)(5² + 8)(8² + 8)(10² + 8)(16² + 8)
= (2² + 8)(6² + 8)(28² + 8)(44² + 8) = (2² - 1)(5² - 1)(7² - 1)(485² - 1).

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

28518

28518² = (2² + 3)(5² + 3)(12² + 3)(168² + 3).

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

28536

28536² = (2² - 1)(5² - 1)(3363² - 1).

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

28560

28560² = (2² - 1)(15² - 1)(16² - 1)(69² - 1) = (2² - 1)(69² - 1)(239² - 1).

13⁴ + 28560 = 239², 13⁴ - 28560 = 1².

Page of Squares : First Upload April 28, 2012 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

28561

28561 = 169² is a square with different digits.

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28582

28582² = 816930724 is a square with different digits.

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28585

28585² = 817102225, and 81 = 9², 7102225 = 2665².

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28600

28600²= 101 x 102 + 102 x 103 + 103 x 104 + ... + 1348 x 1349.

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28604

28604² = 818188816 is a square with 3 kinds of digits.

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28632

28632²± 5 are primes.

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

28644

28644² = (4² + 6)(6² + 6)(26² + 6)(36² + 6).

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

28666

28666²± 3 are primes.

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

28672

28672² = (1² + 7)(5² + 7)(7² + 7)(11² + 7)(21² + 7) = (7² + 7)(21² + 7)(181² + 7).

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

28674

28674² = (2² + 2)(23² + 2)(508² + 2).

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

28676

28676²± 3 are primes.

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

28686

28686² = (17² + 5)(1673² + 5) = (3² + 5)(4² + 5)(1673² + 5).

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

28721

28721² = 60⁴ + 135⁴ + 148⁴ (the third primitive identity).

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28724

28724² = 2884² + 2885² + 2886² + ... + 2979².

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28728

28728² = (2² - 1)(3² - 1)(8² - 1)(20² - 1)(37² - 1) = (5² - 1)(8² - 1)(20² - 1)(37² - 1).

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

28730

28730² = (1² + 1)(2² + 1)(38² + 1)(239² + 1) = (2² + 1)(4² + 1)(13² + 1)(239² + 1)
= (3² + 1)(38² + 1)(239² + 1) = (5² + 1)(21² + 1)(268² + 1).

Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013
by Yoshio Mimura, Kobe, Japan

28731

28731² = 825470361 is a square with different digits.

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28742

28742²± 3 are primes.

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

28743

28743² = 1363² + 1365² + 1367² + 1369² + ... + 1955².

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28756

28756² = (19² + 3)(32² + 3)(47² + 3) = (2² + 3)(7² + 3)(32² + 3)(47² + 3).

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

28761

28761²± 2 are primes.

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

28774

28774²± 3 are primes.

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

28793

A cubic polynomial:
(X + 756²)(X + 4048²)(X + 28497²) = X³ + 28793²X² + 117390252²X + 87209027136².

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28800

28800² = (19² - 1)(31² - 1)(49² - 1) = (2² - 1)(11² - 1)(31² - 1)(49² - 1)
= (2² - 1)(3² - 1)(4² - 1)(31² - 1)(49² - 1) = (3² - 1)(11² - 1)(19² - 1)(49² - 1)
= (3² - 1)(4² - 1)(5² - 1)(11² - 1)(49² - 1) = (4² - 1)(5² - 1)(31² - 1)(49² - 1)
= (4² - 1)(9² - 1)(17² - 1)(49² - 1).

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

28822

28822²± 3 are primes.

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

28827

28827²± 2 are primes.

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

28832

28832²± 3 are primes.

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

28836

28836² = (1² + 8)(9² + 8)(10² + 8)(98² + 8).

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

28874

28822²± 3 are primes.

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

28875

28875² = (1² + 6)(3² + 6)(13² + 6)(213² + 6) = (3² + 6)(13² + 6)(15² + 6)(37² + 6)
= (3² + 6)(7² + 6)(27² + 6)(37² + 6).

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

28888

28888²± 3 are primes.

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

28908

28908² = (2² + 8)(49² + 8)(170² + 8).

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

28910

28910² = (1² + 6)(8² + 6)(17² + 6)(76² + 6) = (17² + 6)(22² + 6)(76² + 6).

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

28917

28917²± 2 are primes.

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

28927

1² + 2² + 3² + 4² + ... + 28927² = 8068846468480, which consists of even digits.

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan

28938

28938²± 5 are primes.

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

28980

28980² = 80*81*82 + 81*82*83 + 82*83*84 + 83*84*85 + ... + 240*241*242.

28980² = (1² + 5)(15² + 5)(25² + 5)(31² + 5) = (1² + 5)(3² + 5)(4² + 5)(5² + 5)(8² + 5)(15² + 5)
= (1² + 5)(3² + 5)(5² + 5)(15² + 5)(38² + 5) = (1² + 5)(3² + 5)(8² + 5)(15² + 5)(25² + 5)
= (1² + 5)(4² + 5)(5² + 5)(15² + 5)(31² + 5) = (1² + 5)(5² + 5)(8² + 5)(15² + 5)(17² + 5)
= (2² + 5)(3² + 5)(5² + 5)(15² + 5)(31² + 5) = (22² - 1)(24² - 1)(55² - 1)
= (3² + 5)(5² + 5)(8² + 5)(11² + 5)(15² + 5) = (5² + 5)(11² + 5)(15² + 5)(31² + 5)
= (7² - 1)(8² - 1)(22² - 1)(24² - 1).

Page of Squares : First Upload October 26, 2103 ; Last Revised February 15, 2014
by Yoshio Mimura, Kobe, Japan

28998

28998² = 840884004 is a square with 3 kinds of even digits.

Page of Squares : First Upload April 28, 2012 ; Last Revised April 28, 2012
by Yoshio Mimura, Kobe, Japan