Squares:25000s

25010

25010² = (1² + 1)(11² + 1)(32² + 1)(50² + 1).

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

25014

25014² = (2² + 2)(8² + 2)(1257² + 2).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25024

S2(25024) = S2(7) * S2(33) * S2(207), where S2(n) = 1² + 2² + 3² + ... + n².

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25040

25040²= 1081 x 1082 + 1082 x 1083 + 1083 x 1084 +...+ 1464 x 1465.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25041

25041²± 2 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25045

25045 = 627252025 is a square pegged by 2.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25059

25059² = 627953481 is a square with different digits.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25068

25068² = 628404624 is a square with even digits.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25185

25185² = 183² + 184² + 185² + ... + 1240².

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25089

25089²± 2 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25090

25090² = (3² + 4)(31² + 4)(224² + 4).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25092

25092² = (1² + 8)(3² + 8)(14² + 8)(142² + 8) = (3² + 8)(14² + 8)(19² + 8)(22² + 8).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25112

25112² = (1² + 3)(13² + 3)(17² + 3)(56² + 3).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25160

25160² = (1² + 4)(4² + 4)(8² + 4)(12² + 4)(25² + 4).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25200

25200² = (2² - 1)(4² - 1)(15² - 1)(251² - 1) = (2² - 1)(4² - 1)(6² - 1)(13² - 1)(49² - 1)
= (2² - 1)(4² - 1)(6² - 1)(9² - 1)(71² - 1) = (3² - 1)(4² - 1)(6² - 1)(15² - 1)(26² - 1)
= (3² - 1)(4² - 1)(6² - 1)(8² - 1)(49² - 1) = (6² - 1)(11² - 1)(15² - 1)(26² - 1)
= (6² - 1)(17² - 1)(251² - 1) = (6² - 1)(8² - 1)(11² - 1)(49² - 1).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25227

25227² = 9³ + 75³ + 462³ + 813³.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25272

25272² = 4! + 5! + 7! + 11! + 11! + 11! + 11! + 12!.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25275

25275² = 1027² + 1029² + 1031² + 1033² + ... + 1699².

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25279

25279² = 639027841 is a square with different digits.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25281

25281 = 159² is a zigzag square.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25284

25284² = (1² + 3)(2² + 3)(12² + 3)(13² + 3)(30² + 3) = (1² + 3)(2² + 3)(30² + 3)(159² + 3)
= (12² + 3)(13² + 3)(159² + 3) = (5² + 3)(12² + 3)(13² + 3)(30² + 3) = (5² + 3)(30² + 3)(159² + 3).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25300

25300² = 640090000, and 6400 = 80², 90000 = 300².

25300² = 531² + 533² + 535² + 537² + 539² + ... + 1585².

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25307

25307² = 640444249 is a square pegged by 4.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25314

25314²± 5 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25326

25326² = (1² + 5)(2² + 5)(4² + 5)(14² + 5)(53² + 5) = (2² + 5)(11² + 5)(14² + 5)(53² + 5)
= (2² + 5)(7² + 5)(14² + 5)(81² + 5) = (4² + 5)(7² + 5)(14² + 5)(53² + 5).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

253300

25330² = (1² + 9)(17² + 9)(464² + 9).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25344

25344² = (17² - 1)(23² - 1)(65² - 1).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25350

25350² = (1² + 9)(2² + 9)(41² + 9)(54² + 9) = (11² + 9)(41² + 9)(54² + 9)
= (2² + 9)(41² + 9)(171² + 9).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25377

25377²± 2 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25378

25378² = 644042884 is a square with even digits.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25380

25380² = (1² + 5)(5² + 5)(29² + 5)(65² + 5).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25398

25398² = (1² + 2)(2² + 2)(7² + 2)(9² + 2)(92² + 2) = (4² + 2)(7² + 2)(9² + 2)(92² + 2).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25408

25408² = 645566464 is a square which consists of 3 kinds of digits.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25410

25410² = (1² + 6)(3² + 6)(4² + 6)(18² + 6)(29² + 6) = (1² + 6)(4² + 6)(7² + 6)(15² + 6)(18² + 6)
= (15² + 6)(18² + 6)(92² + 6) = (18² + 6)(29² + 6)(48² + 6) = (2² + 6)(15² + 6)(18² + 6)(29² + 6)
= (2² + 6)(3² + 6)(4² + 6)(15² + 6)(29² + 6) = (3² + 6)(4² + 6)(15² + 6)(92² + 6)
= (3² + 6)(4² + 6)(29² + 6)(48² + 6) = (3² + 6)(4² + 6)(6² + 6)(7² + 6)(29² + 6)
= (4² + 6)(12² + 6)(15² + 6)(29² + 6) = (4² + 6)(7² + 6)(15² + 6)(48² + 6)
= (6² + 6)(7² + 6)(18² + 6)(29² + 6).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25416

25416²± 5 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25419

(25419² + 7) = (1² + 7)(2² + 7)(4² + 7)(5² + 7)(6² + 7)(15² + 7).

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25430

25430²± 3 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25440

25440²= 226 x 227 + 227 x 228 + 228 x 229 + ... + 1249 x 1250.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25488

25488² = (4² + 8)(8² + 8)(13² + 8)(46² + 8).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25500

25500² = (1² + 9)(4² + 9)(5² + 9)(9² + 9)(29² + 9).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25515

25515² = (2² + 5)(10² + 5)(830² + 5).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25542

25542² = (1² + 2)(14² + 2)(1048² + 2) = (1² + 2)(2² + 2)(3² + 2)(16² + 2)(113² + 2)
= (1² + 2)(2² + 2)(59² + 2)(102² + 2) = (1² + 2)(3² + 2)(4² + 2)(1048² + 2)
= (1² + 2)(8² + 2)(16² + 2)(113² + 2) = (14² + 2)(16² + 2)(113² + 2)
= (3² + 2)(4² + 2)(16² + 2)(113² + 2) = (3² + 2)(8² + 2)(16² + 2)(59² + 2)
= (4² + 2)(59² + 2)(102² + 2).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25544

25544²± 3 are primes.

25544² = (1² + 3)(10² + 3)(11² + 3)(113² + 3).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25572

25572² = 653927184 is a square with different digits.

25572² = (2² + 8)(7382² + 8).

Page of Squares : First Upload April 7, 2012 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25574

25574²± 3 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25578

25578² = (1² + 5)(4² + 5)(32² + 5)(71² + 5) = (11² + 5)(32² + 5)(71² + 5)
= (2² + 5)(3² + 5)(32² + 5)(71² + 5) = (3² + 5)(13² + 5)(16² + 5)(32² + 5).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25604

25604² = (12² + 4)(13² + 4)(160² + 4)

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25610

25610²± 3 are primes.

25610² = (1² + 1)(2² + 1)(14² + 1)(577² + 1)
= (1² + 1)(3² + 1)(14² + 1)(408² + 1) = (3² + 1)(14² + 1)(577² + 1).

Page of Squares : First Upload November 9, 2013 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25628

25628² = 2568² + 2569² + 2570² + ... + 2663².

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25634

25634² = 1632 x 1633 + 1634 x 1635 + 1636 x 1637 + 1638 x 1639 + ... + 2022 x 2023.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25636

25636² = (1² + 1)(4² + 1)(5² + 1)(21² + 1)(41² + 1).

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

25652

14652³ + 25641³ = 4472523².

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25653

25653²± 2 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25696

25696²± 3 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25707

25707² = (1² + 2)(3² + 2)(63² + 2)(71² + 2).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25726

25726²± 3 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25738

25738² = 662444644 is a square with 3 kinds of even digits.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25740

25740² = (2² - 1)(12² - 1)(14² - 1)(89² - 1) = (2² - 1)(4² - 1)(12² - 1)(14² - 1)(23² - 1)
= (2² - 1)(9² - 1)(10² - 1)(12² - 1)(14² - 1).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25754

25754²± 3 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25767

25767²± 2 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25771

25771² = 664144441 is a square which consists of 3 kinds of digits.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25810

25810² = (5² + 4)(24² + 4)(199² + 4) = (7² + 9)(13² + 9)(254² + 9).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25824

25824² = 666878976, a square every digit of which is greater than 5.

Page of Squares : First Upload September 18, 2013 ; Last Revised September 18, 2013
by Yoshio Mimura, Kobe, Japan

25830

25830² = (1² + 5)(4² + 5)(6² + 5)(10² + 5)(35² + 5) = (2² + 5)(3² + 5)(6² + 5)(10² + 5)(35² + 5)
= (4² + 5)(6² + 5)(25² + 5)(35² + 5) = (6² + 5)(10² + 5)(11² + 5)(35² + 5)
= (6² + 5)(35² + 5)(115² + 5).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25839

25839²± 2 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25840

25840² = (9² - 1)(2889² - 1).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25852

25852²± 3 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25858

25858² = 668636164 is a square pegged by 6.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25878

25878²± 5 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25886

25886² = 3905 x 3906 + 3907 x 3908 + 3909 x 3910 + 3911 x 3912 + ... + 3989 x 3990.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25920

25920² = (2² - 1)(5² - 1)(19² - 1)(161² - 1) = (2² - 1)(5² - 1)(7² - 1)(17² - 1)(26² - 1).

246² + 25920 = 294², 246² - 25920 = 186².

Page of Squares : First Upload April 7, 2012 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25925

25925² = (38² + 1)(682² + 1).

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

25926

25926² = (12² + 5)(13² + 5)(161² + 5).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25941

25941² = 672935481 is a square with different digits.

Page of Squares : First Upload April 7, 2012 ; Last Revised April 7, 2012
by Yoshio Mimura, Kobe, Japan

25970

25970² = (1² + 6)(10² + 6)(22² + 6)(43² + 6).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25974

25974² = (15² + 9)(18² + 9)(93² + 9) = (2² + 9)(3² + 9)(18² + 9)(93² + 9).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25984

25984²± 3 are primes.

25984² = (1² + 7)(5² + 7)(7² + 7)(14² + 7)(15² + 7) = (1² + 7)(5² + 7)(7² + 7)(217² + 7)
= (5² + 7)(14² + 7)(15² + 7)(21² + 7) = (5² + 7)(21² + 7)(217² + 7)
= (5² + 7)(7² + 7)(14² + 7)(43² + 7).

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan

25989

25989²± 2 are primes.

Page of Squares : First Upload February 12, 2014 ; Last Revised February 12, 2014
by Yoshio Mimura, Kobe, Japan