Squares:19000s

19000

19000² = 361000000, 36 = 6², 1000000 = 1000².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19005

19005² = 4² + 5² + ... + 38² = 39² + 40² + ... + 48².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19008

19008² = (2² + 8)(4² + 8)(6² + 8)(10² + 8)(16² + 8) = (2² - 1)(10² - 1)(17² - 1)(65² - 1)
= (2² - 1)(3² - 1)(10² - 1)(17² - 1)(23² - 1) = (4² + 8)(8² + 8)(16² + 8)(28² + 8)
= (5² - 1)(10² - 1)(17² - 1)(23² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19023

19023² = 361874529 is a square consisting of different digits.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19025

19025² = 361950625, 361 = 19², 950625 = 975².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19030

19030² = (2² + 6)(4² + 6)(1283² + 6).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19038

19038²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19050

19050² = (11² + 6)(12² + 6)(138² + 6) = (2² + 6)(3² + 6)(11² + 6)(138² + 6).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19056

19056² = 363131136 is a square consisting of 3 kinds of digits.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19069

19069² = 363626761 is a square pegged by 6.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19071

19071² = 58³ + 64³ + 92³ + 713³.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19116

19116² = (1² + 8)(10² + 8)(13² + 8)(46² + 8).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19125

19125²± 2 are primes.

19125² = (4² + 9)(6² + 9)(12² + 9)(46² + 9).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19152

19152² = (2² - 1)(15² - 1)(20² - 1)(37² - 1) = (2² - 1)(5² - 1)(20² - 1)(113² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19173

19173²± 2 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19179

19179² = (5² + 2)(3691² + 2).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19204

19204² = 7837 * 7838 + 7838 * 7839 + 7839 * 7840 + ... + 7842 * 7843.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19206

19206²± 5 are primes.

19206² = (1² + 2)(2² + 2)(3² + 2)(17² + 2)(80² + 2) = (1² + 2)(8² + 2)(17² + 2)(80² + 2)
= (14² + 2)(17² + 2)(80² + 2) = (3² + 2)(4² + 2)(17² + 2)(80² + 2).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19210

19210² = (1² + 1)(2² + 1)(4² + 1)(15² + 1)(98² + 1)
= (13² + 1)(15² + 1)(98² + 1) = (3² + 1)(4² + 1)(15² + 1)(98² + 1).

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

19224

19224² = (1² + 8)(8² + 8)(9² + 8)(80² + 8) = (44² + 8)(436² + 8).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19240

19240² = (1² + 4)(2² + 4)(49² + 4)(62² + 4) = (1² + 4)(3² + 4)(10² + 4)(234² + 4)
= (2² + 4)(29² + 4)(234² + 4) = (3² + 4)(62² + 4)(86² + 4) = (6² + 4)(49² + 4)(62² + 4).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19250

19250²± 3 are primes.

19250² = (1² + 6)(2² + 6)(37² + 6)(62² + 6) = (1² + 6)(2² + 6)(4² + 6)(13² + 6)(37² + 6)
= (1² + 6)(2² + 6)(7² + 6)(8² + 6)(37² + 6) = (2² + 6)(7² + 6)(13² + 6)(62² + 6)
= (2² + 6)(7² + 6)(22² + 6)(37² + 6) = (4² + 6)(8² + 6)(13² + 6)(37² + 6)
= (8² + 6)(37² + 6)(62² + 6).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19264

19264²± 3 are primes.

19264² = (1² + 7)(6² + 7)(21² + 7)(49² + 7).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19272

19272² = (16² + 8)(24² + 8)(49² + 8).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19278

19278²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19320

19320² = (3² - 1)(13² - 1)(22² - 1)(24² - 1).

19320² = (1³)(2³ + 3³ + 4³ + ... + 13³)(14³ + 15³ + 16³ + ... + 21³).

Page of Squares : First Upload February 9, 2013 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19328

19328² = (1² + 7)(3² + 7)(12² + 7)(139² + 7) = (11² + 7)(12² + 7)(139² + 7).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19358

19358²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19370

19370²± 3 are primes.

19370² = (3² + 4)(61² + 4)(88² + 4).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19377

19377² = 375468129 is a square consisting of different digits.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19380

19380² = (2² - 1)(16² - 1)(18² - 1)(39² - 1) = (2² - 1)(4² - 1)(2889² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19408

19408² = S2(547) + S2(988), where S2(n) = 1² + 2² + 3² + ... + n².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19450

19450²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19497

19497²± 2 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19523

19523² = (1² + 6)(7379² + 6).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19526

19526²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19529

19529² = 1379² + 1380² + 1381² + ... + 1555².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19558

19558² = (4² + 6)(11² + 6)(370² + 6).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19569

19569² = 382945761 is a square consisting of different digits.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19584

19584² = (17² - 1)(33² - 1)(35² - 1) = (2² - 1)(3² - 1)(7² - 1)(577² - 1)
= (5² - 1)(7² - 1)(577² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19602

19602² = (1² + 2)(2² + 2)(3² + 2)(5² + 2)(14² + 2)(19² + 2)
= (1² + 2)(3² + 2)(4² + 2)(5² + 2)(8² + 2)(19² + 2) = (1² + 2)(3² + 2)(8² + 2)(19² + 2)(22² + 2)
= (1² + 2)(4² + 2)(19² + 2)(140² + 2) = (1² + 2)(5² + 2)(8² + 2)(14² + 2)(19² + 2)
= (3² + 2)(14² + 2)(19² + 2)(22² + 2) = (3² + 2)(4² + 2)(5² + 2)(14² + 2)(19² + 2)
= (3² + 2)(5² + 2)(8² + 2)(140² + 2).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19608

19608² = (11² + 8)(12² + 8)(140² + 8) = (13² + 3)(15² + 3)(99² + 3)
= (3² + 3)(4² + 3)(13² + 3)(99² + 3).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19610

19610² = (1² + 4)(7² + 4)(12² + 4)(99² + 4).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19618

19618² = (24² + 2)(816² + 2).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19629

19629² = 1 + 3 + 6 + 10 + 15 + 21 + ... + 1176 (the sum of tetrahedrals).

19629² = 385297641 is a square consisting of different digits.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19635

19635² = (2² - 1)(6² - 1)(16² - 1)(120² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19656

19656² = (2² - 1)(8² - 1)(27² - 1)(53² - 1) = (2³ + 1)(3³ + 1)(5³ + 1)(23³ + 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19662

19662²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19684

19684² = (1² + 3)(2² + 3)(4² + 3)(16² + 3)(53² + 3) = (16² + 3)(23² + 3)(53² + 3)
= (4² + 3)(5² + 3)(16² + 3)(53² + 3).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19695

19695² = 3850² + 3851² + 3852² + ... + 3875².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19698

19698² = (14² + 5)(17² + 5)(81² + 5) = (2² + 3)(8² + 3)(12² + 3)(75² + 3)
= (3² + 5)(4² + 5)(14² + 5)(81² + 5) = (4² + 5)(53² + 5)(81² + 5).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19701

19701² = 1144² + 1145² + 1146² + ... + 1385².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19707

19707²± 2 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19708

19708²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19710

19710² = (3² + 9)(6² + 9)(8² + 9)(81² + 9).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19712

19712² = (1² + 7)(2² + 7)(7² + 7)(13² + 7)(21² + 7) = (1² + 7)(9² + 7)(21² + 7)(35² + 7)
= (2² + 7)(3² + 7)(5² + 7)(7² + 7)(35² + 7) = (2² + 7)(3² + 7)(7² + 7)(9² + 7)(21² + 7)
= (3² + 7)(7² + 7)(21² + 7)(31² + 7) = (5² + 7)(7² + 7)(13² + 7)(35² + 7)
= (7² + 7)(35² + 7)(75² + 7) = (7² + 7)(9² + 7)(13² + 7)(21² + 7).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19720

19720² = (9² + 4)(26² + 4)(82² + 4).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19737

19737² = (1² + 2)(7² + 2)(27² + 2)(59² + 2).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19740

19740² = (9² - 1)(46² - 1)(48² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19741

19741² = 344² + 345² + 346² + ... + 1065².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19778

19778² = (5² + 6)(26² + 6)(136² + 6).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19782

19782² = 3³ + 48³ + 156³ + 729³.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19803

19803² = (8² + 5)(2384² + 5).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19812

19812²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19825

19825² = (28² + 9)(704² + 9).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19845

19845² = (2² + 5)(10² + 5)(20² + 5)(32² + 5) = (2² - 1)(6² - 1)(8² - 1)(244² - 1).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19855

19855² = 55² + 56² + ... + 60² = 61² + 62² + ... + 65².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19875

19875²± 2 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19880

19880²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19881

19881²± 2 are primes.

19881 is a square (141²) consisting of 3 kinds of digits.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19883

19883² = 1315² + 1317² + 1319² + 1321² + ... + 1667².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19890

19890² = (1² + 9)(2² + 9)(12² + 9)(141² + 9) = (1² + 9)(2² + 9)(15² + 9)(114² + 9)
= (1² + 9)(2² + 9)(5² + 9)(12² + 9)(24² + 9) = (11² + 9)(12² + 9)(141² + 9)
= (11² + 9)(15² + 9)(114² + 9) = (12² + 9)(39² + 9)(41² + 9)
= (2² + 9)(11² + 9)(12² + 9)(39² + 9) = (2² + 9)(12² + 9)(15² + 9)(29² + 9)
= (2² + 9)(3² + 9)(11² + 9)(114² + 9) = (2² + 9)(39² + 9)(141² + 9)
= (2² + 9)(4² + 9)(5² + 9)(12² + 9)(15² + 9) = (2² + 9)(5² + 9)(24² + 9)(39² + 9)
= (2² + 9)(5² + 9)(6² + 9)(11² + 9)(12² + 9) = (2² + 9)(5² + 9)(6² + 9)(141² + 9)
= (3² + 9)(12² + 9)(379² + 9) = (3² + 9)(41² + 9)(114² + 9) = (3² + 9)(5² + 9)(804² + 9)
= (5² + 9)(11² + 9)(12² + 9)(24² + 9) = (5² + 9)(24² + 9)(141² + 9)
= (5² + 9)(54² + 9)(63² + 9) = (5² + 9)(6² + 9)(12² + 9)(41² + 9).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19893

19893² = 377² + 378² + 379² + ... + 1074².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19909

19909² = 925³ - 924³ + 923³ - 922³ + ... + 1³.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19912

19912² = 802² + 803² + 804² + ... + 1194².

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19926

19926² = (2² + 2)(5² + 2)(22² + 2)(71² + 2).

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19928

(19928² + 6) = (1² + 6)(5² + 6)(7² + 6)(11² + 6)(16² + 6).

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19930

19930²± 3 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19938

19938²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan

19940

19940, 19941, 19942, 19943 and 19944 are consecutive integers having square factors (the 10th case).

Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan

19950

19950² = 1225 * 1226 + 1227 * 1228 + 1229 * 1230 + 1231 * 1232 + ... + 1615 * 1616.

Page of Squares : First Upload February 18, 2012 ; Last Revised February 18, 2012
by Yoshio Mimura, Kobe, Japan

19962

19962²± 5 are primes.

Page of Squares : First Upload February 1, 2014 ; Last Revised February 1, 2014
by Yoshio Mimura, Kobe, Japan