Squares:34000s

34000

34000² = (1² + 4)(2² + 4)(6² + 4)(8² + 4)(9² + 4)(11² + 4)
= (1² + 4)(2² + 4)(6² + 4)(11² + 4)(76² + 4) = (1² + 4)(4² + 4)(9² + 4)(14² + 4)(26² + 4)
= (1² + 4)(6² + 4)(8² + 4)(11² + 4)(26² + 4) = (2² + 4)(4² + 4)(9² + 4)(11² + 4)(26² + 4)
= (2² + 4)(8² + 4)(9² + 4)(11² + 4)(14² + 4) = (2² + 4)(11² + 4)(14² + 4)(76² + 4)
= (8² + 4)(11² + 4)(14² + 4)(26² + 4).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34010

34010²= 70 x 71 + 71 x 72 + 72 x 73 + ... + 1513 x 1514.

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34020

34020² = (1² + 5)(2² + 5)(3² + 5)(5² + 5)(11² + 5)(20² + 5)
= (1² + 5)(2² + 5)(4² + 5)(5² + 5)(7² + 5)(25² + 5)
= (1² + 5)(2² + 5)(5² + 5)(7² + 5)(10² + 5)(11² + 5) = (1² + 5)(2² + 5)(5² + 5)(7² + 5)(115² + 5)
= (1² + 5)(3² + 5)(4² + 5)(5² + 5)(7² + 5)(20² + 5) = (1² + 5)(3² + 5)(7² + 5)(20² + 5)(25² + 5)
= (3² + 5)(5² + 5)(7² + 5)(11² + 5)(20² + 5) = (2² + 5)(5² + 5)(7² + 5)(11² + 5)(25² + 5)
= (1² + 5)(5² + 5)(7² + 5)(17² + 5)(20² + 5) = (1² + 5)(5² + 5)(25² + 5)(101² + 5).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34034

34034² = 379² + 380² + 381² + ... + 1522².

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34048

34048²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34056

34056² = (1² + 8)(4² + 8)(11² + 8)(204² + 8) = (4² + 8)(28² + 8)(247² + 8)
= (5² + 8)(11² + 8)(16² + 8)(32² + 8) = (8² + 8)(16² + 8)(247² + 8) = (16² + 8)(2096² + 8).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34071

34071²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34076

34076²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34080

34080²= 4009 x 4010 + 4010 x 4011 + 4011 x 4012 + ... + 4079 x 4080.

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34099

34099² = 329² + 331² + 333² + 335² + ... + 1913².

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34100

34100² = (2² + 6)(4² + 6)(26² + 6)(88² + 6).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34125

34125² = 246² + 247² + 248² + ... + 1519².

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34188

34188² = 351² + 353² + 355² + 357² + ... + 1917².

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34203

34203²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34228

34228² = (13² + 3)(14² + 3)(185² + 3).

(34228² - 8) = (3² - 8)(4² - 8)(7² - 8)(9² - 8)(11² - 8)(21² - 8).

Page of Squares : First Upload June 9, 2012 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34272

34272² = (3² - 1)(7² - 1)(35² - 1)(50² - 1).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34314

34314² = (2² + 3)(4² + 3)(30² + 3)(99² + 3).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34320

34320² = (2² - 1)(12² - 1)(21² - 1)(79² - 1) = (9² - 1)(12² - 1)(14² - 1)(23² - 1).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34336

34336² = (1² + 7)(15² + 7)(797² + 7) = (15² + 7)(17² + 7)(131² + 7) = (43² + 7)(797² + 7).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34370

34370² = (1² + 6)(2² + 6)(4108² + 6) = (8² + 6)(4108² + 6).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34430

34430² = 1788² + 1789² + 1790² + ... + 2100².

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34440

34440² = (2² - 1)(6² - 1)(3361² - 1).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34450

34450² = (18² + 1)(23² + 1)(83² + 1) = (2² + 1)(8² + 1)(23² + 1)(83² + 1)
= (1² + 9)(2² + 9)(4² + 9)(16² + 9)(37² + 9) = (4² + 9)(11² + 9)(16² + 9)(37² + 9).

Page of Squares : First Upload November 9, 2013 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34461

34461²± 2 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34504

34504²= 967 x 968 + 968 x 969 + 969 x 970 + ... + 1647 x 1648.

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34518

34518²± 5 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34520

34520²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34534

34534² = (1²)(2²)(3² + 4³ + 5³ + ... + 963²).

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

34560

204² + 34560 = 276², 204² - 34560 = 84².

34560² = (2² - 1)(3² - 1)(5² - 1)(7² - 1)(11² - 1)(19² - 1) = (2² - 1)(3² - 1)(5² - 1)(9² - 1)(161² - 1)
= (2² - 1)(4² - 1)(5² - 1)(7² - 1)(9² - 1)(17² - 1) = (2² - 1)(5² - 1)(7² - 1)(19² - 1)(31² - 1)
= (2² - 1)(7² - 1)(9² - 1)(17² - 1)(19² - 1) = (3² - 1)(7² - 1)(11² - 1)(161² - 1)
= (7² - 1)(31² - 1)(161² - 1).

Page of Squares : First Upload June 9, 2012 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34578

34578² = (1² + 2)(2² + 2)(26² + 2)(313² + 2) = (4² + 2)(26² + 2)(313² + 2).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34596

34596 = 186² is a square with different digits.

34596²± 5 are primes.

Page of Squares : First Upload June 9, 2012 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34600

34600² = (1² + 4)(6² + 4)(13² + 4)(186² + 4) = (13² + 4)(14² + 4)(186² + 4).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34608

34608² = (1² + 3)(3² + 3)(5² + 3)(10² + 3)(93² + 3).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34634

34634² = 1199513956, a square with odd digits except the last digit 6.

Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013
by Yoshio Mimura, Kobe, Japan

34641

34641² = 1199998881 is a square with 3 kinds of digits.

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34642

34642²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34650

34650² = (1² + 6)(3² + 6)(12² + 6)(15² + 6)(18² + 6) = (3² + 6)(6² + 6)(7² + 6)(12² + 6)(15² + 6)
= (3² + 6)(12² + 6)(15² + 6)(48² + 6).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34656

190² + 34656 = 266², 190² - 34656 = 38².

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34670

34670²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34680

221² + 34680 = 289², 221² - 34680 = 119².

34³ + 34680 = 272², 34³ - 34680 = 68².

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34686

34686² = (1² + 5)(6² + 5)(29² + 5)(76² + 5).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34710

34710² = (2² + 9)(9² + 9)(13² + 9)(76² + 9).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34776

34776² = (2² - 1)(3² - 1)(22² - 1)(323² - 1) = (5² - 1)(22² - 1)(323² - 1).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34784

34784² = (5² + 7)(6149² + 7).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34827

34827² = 1212919929 is a square with 3 kinds of digits.

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34830

34830² = (5² + 5)(9² + 5)(20² + 5)(34² + 5).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34840

34840²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34848

34848² = (4² + 8)(6² + 8)(28² + 8)(38² + 8) = (6² + 8)(8² + 8)(16² + 8)(38² + 8).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34850

34850² = (1² + 1)(2² + 1)(4² + 1)(7² + 1)(378² + 1) = (1² + 1)(2² + 1)(9² + 1)(32² + 1)(38² + 1)
= (2² + 1)(3² + 1)(13² + 1)(378² + 1) = (2² + 1)(3² + 1)(4² + 1)(9² + 1)(132² + 1)
= (2² + 1)(4² + 1)(9² + 1)(13² + 1)(32² + 1) = (2² + 1)(9² + 1)(13² + 1)(132² + 1)
= (3² + 1)(4² + 1)(7² + 1)(378² + 1) = (3² + 1)(9² + 1)(32² + 1)(38² + 1)
= (4² + 1)(7² + 1)(9² + 1)(132² + 1) = (7² + 1)(13² + 1)(378² + 1)
= (1² + 4)(59² + 4)(264² + 4) = (9² + 4)(59² + 4)(64² + 4).

Page of Squares : First Upload November 9, 2013 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34856

34856²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34866

34866² = (2² + 9)(3² + 9)(17² + 9)(132² + 9) = (15² + 9)(17² + 9)(132² + 9).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34874

34874²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34881

34881² = (15² + 6)(2295² + 6).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34884

34884² = (1² + 8)(2² + 8)(3² + 8)(26² + 8)(31² + 8)
= (1² + 2)(2² + 2)(4² + 2)(6² + 2)(7² + 2)(44² + 2)
= (1² + 2)(2² + 2)(4² + 2)(6² + 2)(13² + 2)(24² + 2) = (1² + 8)(2² + 8)(7² + 8)(14² + 8)(31² + 8)
= (1² + 8)(2² + 8)(14² + 8)(235² + 8) = (1² + 8)(3² + 8)(7² + 8)(14² + 8)(26² + 8)
= (1² + 2)(4² + 2)(6² + 2)(24² + 2)(32² + 2) = (1² + 8)(14² + 8)(26² + 8)(31² + 8)
= (2² + 8)(3² + 8)(7² + 8)(10² + 8)(31² + 8) = (2² + 8)(3² + 8)(10² + 8)(235² + 8)
= (2² + 2)(5² + 2)(6² + 2)(10² + 2)(44² + 2) = (2² + 2)(6² + 2)(7² + 2)(10² + 2)(32² + 2)
= (2² + 2)(10² + 2)(32² + 2)(44² + 2) = (3² + 8)(10² + 8)(26² + 8)(31² + 8)
= (7² + 8)(10² + 8)(14² + 8)(31² + 8) = (10² + 8)(14² + 8)(235² + 8).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34892

34892²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34932

34932² = (7² - 1)(5042² - 1).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34934

34934²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34944

34944² = (7² - 1)(15² - 1)(337² - 1).

340² + 34944 = 388², 340² - 34944 = 284².

Page of Squares : First Upload June 9, 2012 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34954

34954²± 3 are primes.

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34960

34960²= 401 x 402 + 402 x 403 + 403 x 404 + ... + 1550 x 1551.

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34962

34962² = 1222341444, a square every digit of which is non-zero and smaller than 5.

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

34965

34965² = 1222551225 is a square with 3 kinds of digits.

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan

34974

34974² = (13² + 5)(14² + 5)(187² + 5).

Page of Squares : First Upload February 22, 2014 ; Last Revised February 22, 2014
by Yoshio Mimura, Kobe, Japan

34992

34992² = 1927² + 1929² + 1931² + 1933² + ... + 2437².

Page of Squares : First Upload June 9, 2012 ; Last Revised June 9, 2012
by Yoshio Mimura, Kobe, Japan