Squares:90000s

90001

90001² = 8100180001, a square with 3 kinds of digits.

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90075

90075² = 8113505625, and 81 = 9², 13505625 = 3675².

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90100

90100² = (1² + 1)(2² + 1)(3² + 1)(13² + 1)(23² + 1)(30² + 1)
= (1² + 1)(3² + 1)(4² + 1)(7² + 1)(23² + 1)(30² + 1) = (1² + 1)(7² + 1)(13² + 1)(23² + 1)(30² + 1)
= (1² + 4)(7² + 4)(8² + 4)(11² + 4)(60² + 4).

Page of Squares : First Upload November 16, 2013 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90112

90112² = (1² + 7)(2² + 7)(3² + 7)(13² + 7)(181² + 7) = (1² + 7)(2² + 7)(5² + 7)(9² + 7)(181² + 7)
= (1² + 7)(2² + 7)(53² + 7)(181² + 7) = (1² + 7)(3² + 7)(5² + 7)(9² + 7)(11² + 7)(13² + 7)
= (1² + 7)(3² + 7)(9² + 7)(11² + 7)(75² + 7) = (1² + 7)(3² + 7)(11² + 7)(13² + 7)(53² + 7)
= (1² + 7)(5² + 7)(9² + 7)(11² + 7)(53² + 7) = (1² + 7)(5² + 7)(31² + 7)(181² + 7)
= (2² + 7)(11² + 7)(13² + 7)(181² + 7) = (3² + 7)(5² + 7)(53² + 7)(75² + 7)
= (3² + 7)(9² + 7)(13² + 7)(181² + 7) = (9² + 7)(53² + 7)(181² + 7).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90125

90125² = 8122515625, and 81225 = 285², 15625 = 125².

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90144

90144² = 8125940736, a square wirh different digits.

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90153

90153² = 8127563409, a square wirh different digits.

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90170

90170² = 1191² + 1192² + 1193² + ... + 2965².

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90196

90196²± 3 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90198

90198² = 8135679204, a square wirh different digits.

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90202

90202²± 3 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90212

90212²= 533 x 534 + 534 x 535 + 535 x 536 + ... + 2906 x 2907.

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90248

90248²± 3 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90252

90252²± 5 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90288

90288² + 88209² = 126225².

90288² = (1² + 8)(2² + 8)(5² + 8)(7² + 8)(12² + 8)(16² + 8)
= (1² + 8)(2² + 8)(6² + 8)(10² + 8)(126² + 8) = (1² + 8)(2² + 8)(6² + 8)(26² + 8)(50² + 8)
= (1² + 8)(2² + 8)(8² + 8)(12² + 8)(83² + 8) = (1² + 8)(4² + 8)(5² + 8)(8² + 8)(126² + 8)
= (1² + 8)(4² + 8)(7² + 8)(16² + 8)(50² + 8) = (1² + 8)(5² + 8)(6² + 8)(7² + 8)(8² + 8)(12² + 8)
= (1² + 8)(5² + 8)(6² + 8)(12² + 8)(64² + 8) = (1² + 8)(5² + 8)(8² + 8)(12² + 8)(50² + 8)
= (1² + 8)(5² + 8)(12² + 8)(16² + 8)(26² + 8) = (1² + 8)(6² + 8)(12² + 8)(368² + 8)
= (1² + 8)(7² + 8)(8² + 8)(12² + 8)(38² + 8) = (1² + 8)(8² + 8)(28² + 8)(126² + 8)
= (1² + 8)(12² + 8)(38² + 8)(64² + 8) = (2² + 8)(4² + 8)(7² + 8)(8² + 8)(83² + 8)
= (2² + 8)(4² + 8)(64² + 8)(83² + 8) = (2² + 8)(5² + 8)(12² + 8)(368² + 8)
= (2² + 8)(6² + 8)(7² + 8)(10² + 8)(50² + 8) = (2² + 8)(7² + 8)(12² + 8)(16² + 8)(17² + 8)
= (2² + 8)(7² + 8)(12² + 8)(280² + 8) = (4² + 8)(5² + 8)(6² + 8)(7² + 8)(64² + 8)
= (4² + 8)(5² + 8)(7² + 8)(8² + 8)(50² + 8) = (4² + 8)(5² + 8)(7² + 8)(16² + 8)(26² + 8)
= (4² + 8)(5² + 8)(50² + 8)(64² + 8) = (4² + 8)(6² + 8)(7² + 8)(368² + 8)
= (4² + 8)(7² + 8)(38² + 8)(64² + 8) = (4² + 8)(8² + 8)(17² + 8)(126² + 8)
= (4² + 8)(8² + 8)(26² + 8)(83² + 8) = (4² + 8)(50² + 8)(368² + 8)
= (5² + 8)(7² + 8)(10² + 8)(12² + 8)(16² + 8) = (6² + 8)(7² + 8)(28² + 8)(64² + 8)
= (6² + 8)(7² + 8)(8² + 8)(12² + 8)(17² + 8) = (6² + 8)(10² + 8)(26² + 8)(50² + 8)
= (6² + 8)(12² + 8)(17² + 8)(64² + 8) = (7² + 8)(8² + 8)(28² + 8)(50² + 8)
= (7² + 8)(16² + 8)(26² + 8)(28² + 8) = (8² + 8)(10² + 8)(12² + 8)(83² + 8)
= (8² + 8)(12² + 8)(17² + 8)(50² + 8) = (12² + 8)(16² + 8)(17² + 8)(26² + 8)
= (12² + 8)(26² + 8)(280² + 8) = (16² + 8)(44² + 8)(126² + 8) = (28² + 8)(50² + 8)(64² + 8).

Page of Squares : First Upload December 15, 2012 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90378

90378² = 1000² + 1001² + 1002² + ... + 2943².

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90387

90387² = (3² + 2)(9² + 2)(19² + 2)(157² + 2).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90402

90402² = (4² + 3)(6² + 3)(3321² + 3).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90420

90420² = 5098² + 5099² + 5100² + ... + 5394².

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90421

90421² = (4² + 3)(20744² + 3).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90426

90426²± 5 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90475

90475² = 1393² + 1394² + 1395² + ... + 3009².

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90542

90542²± 3 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90546

90546²± 5 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90594

90594²± 5 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90601

90601 = 301², a zigzag square.

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90610

90610² = (1² + 1)(4² + 1)(5² + 1)(8² + 1)(378² + 1) = (1² + 1)(8² + 1)(21² + 1)(378² + 1)
= (2² + 1)(5² + 1)(21² + 1)(378² + 1) = (5² + 1)(47² + 1)(378² + 1)
= (1² + 4)(3² + 4)(8² + 4)(23² + 4)(59² + 4) = (2² + 9)(5² + 9)(14² + 9)(301² + 9).

Page of Squares : First Upload November 16, 2013 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90625

90625² = 8212890625.

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90668

90668² = 8220686224, a square with even digits.

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90720

318² + 90720 = 438², 318² - 90720 = 102².

90720² = (2² - 1)(3² - 1)(4² - 1)(8² - 1)(11² - 1)(55² - 1)
= (2² - 1)(3² - 1)(7² - 1)(8² - 1)(13² - 1)(26² - 1) = (2² - 1)(3² - 1)(7² - 1)(11² - 1)(244² - 1)
= (2² - 1)(3² - 1)(13² - 1)(26² - 1)(55² - 1) = (2² - 1)(4² - 1)(7² - 1)(8² - 1)(13² - 1)(19² - 1)
= (2² - 1)(4² - 1)(8² - 1)(31² - 1)(55² - 1) = (2² - 1)(4² - 1)(13² - 1)(19² - 1)(55² - 1)
= (2² - 1)(5² - 1)(8² - 1)(19² - 1)(71² - 1) = (2² - 1)(6² - 1)(7² - 1)(8² - 1)(161² - 1)
= (2² - 1)(6² - 1)(55² - 1)(161² - 1) = (2² - 1)(7² - 1)(31² - 1)(244² - 1)
= (2² - 1)(8² - 1)(15² - 1)(17² - 1)(26² - 1) = (2² - 1)(8² - 1)(41² - 1)(161² - 1)
= (3² - 1)(4² - 1)(5² - 1)(7² - 1)(244² - 1) = (3² - 1)(4² - 1)(8² - 1)(19² - 1)(55² - 1)
= (3² - 1)(7² - 1)(19² - 1)(244² - 1) = (4² - 1)(5² - 1)(8² - 1)(11² - 1)(55² - 1)
= (5² - 1)(7² - 1)(8² - 1)(13² - 1)(26² - 1) = (5² - 1)(7² - 1)(11² - 1)(244² - 1)
= (5² - 1)(13² - 1)(26² - 1)(55² - 1) = (8² - 1)(11² - 1)(19² - 1)(55² - 1) = (8² - 1)(71² - 1)(161² - 1).

Page of Squares : First Upload December 15, 2012 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90728

90728² = (1² + 7)(32² + 7)(999² + 7).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90729

90729² = (37² + 8)(2445² + 8).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90744

90744² = (1² + 3)(3² + 3)(4² + 3)(14² + 3)(213² + 3) = (1² + 3)(14² + 3)(15² + 3)(213² + 3).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90750

90750² = (2² + 6)(3² + 6)(4² + 6)(7² + 6)(213² + 6) = (2² + 6)(7² + 6)(18² + 6)(213² + 6)
= (3² + 6)(4² + 6)(7² + 6)(18² + 6)(37² + 6) = (4² + 6)(7² + 6)(12² + 6)(213² + 6).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90752

90752²± 3 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90780

90780² = (1² + 9)(5² + 9)(13² + 9)(369² + 9).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90783

90783²± 2 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90794

90794²± 3 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90846

90846² = (1² + 5)(4² + 5)(17² + 5)(472² + 5) = (2² + 5)(3² + 5)(17² + 5)(472² + 5)
= (3² + 5)(4² + 5)(11² + 5)(472² + 5) = (11² + 5)(17² + 5)(472² + 5).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90882

90882² = (1² + 2)(2² + 2)(3² + 2)(4² + 2)(5² + 2)(7² + 2)(41² + 2)
= (1² + 2)(2² + 2)(3² + 2)(7² + 2)(22² + 2)(41² + 2) = (1² + 2)(2² + 2)(4² + 2)(7² + 2)(707² + 2)
= (1² + 2)(2² + 2)(4² + 2)(19² + 2)(265² + 2) = (1² + 2)(2² + 2)(5² + 2)(7² + 2)(14² + 2)(41² + 2)
= (1² + 2)(3² + 2)(4² + 2)(14² + 2)(265² + 2) = (1² + 2)(4² + 2)(5² + 2)(7² + 2)(8² + 2)(41² + 2)
= (1² + 2)(4² + 2)(5² + 2)(41² + 2)(58² + 2) = (1² + 2)(5² + 2)(7² + 2)(10² + 2)(140² + 2)
= (1² + 2)(5² + 2)(19² + 2)(22² + 2)(24² + 2) = (1² + 2)(7² + 2)(8² + 2)(22² + 2)(41² + 2)
= (1² + 2)(22² + 2)(41² + 2)(58² + 2) = (2² + 2)(3² + 2)(5² + 2)(8² + 2)(265² + 2)
= (2² + 2)(5² + 2)(10² + 2)(707² + 2) = (2² + 2)(140² + 2)(265² + 2)
= (3² + 2)(4² + 2)(7² + 2)(22² + 2)(41² + 2) = (4² + 2)(5² + 2)(7² + 2)(14² + 2)(41² + 2)
= (7² + 2)(14² + 2)(22² + 2)(41² + 2).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90884

90884²± 3 are primes.

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90898

90898² = 8262446404, a square with even digits.

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90908

90908² = 8264264464, a square with even digits.

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan

90930

90930² = (1² + 6)(2² + 6)(6² + 6)(1677² + 6) = (6² + 6)(8² + 6)(1677² + 6).

Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014
by Yoshio Mimura, Kobe, Japan

90932

90932² = 8268628624, a square with even digits.

Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012
by Yoshio Mimura, Kobe, Japan