90001
900012 = 8100180001, a square with 3 kinds of digits.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by Yoshio Mimura, Kobe, Japan
90075
900752 = 8113505625, and 81 = 92, 13505625 = 36752.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by 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).
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).
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, 2012by Yoshio Mimura, Kobe, Japan
90144
901442 = 8125940736, a square wirh different digits.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by Yoshio Mimura, Kobe, Japan
90153
901532 = 8127563409, a square wirh different digits.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by Yoshio Mimura, Kobe, Japan
90170
901702 = 11912 + 11922 + 11932 + ... + 29652.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by Yoshio Mimura, Kobe, Japan
90196
901962± 3 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by Yoshio Mimura, Kobe, Japan
90198
901982 = 8135679204, a square wirh different digits.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by Yoshio Mimura, Kobe, Japan
90202
902022± 3 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by 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, 2012by Yoshio Mimura, Kobe, Japan
90248
902482± 3 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by Yoshio Mimura, Kobe, Japan
90252
902522± 5 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by 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).
by Yoshio Mimura, Kobe, Japan
90378
903782 = 10002 + 10012 + 10022 + ... + 29432.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by 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, 2014by Yoshio Mimura, Kobe, Japan
90402
904022 = (42 + 3)(62 + 3)(33212 + 3).
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by Yoshio Mimura, Kobe, Japan
90420
904202 = 50982 + 50992 + 51002 + ... + 53942.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by Yoshio Mimura, Kobe, Japan
90421
904212 = (42 + 3)(207442 + 3).
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by Yoshio Mimura, Kobe, Japan
90426
904262± 5 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by Yoshio Mimura, Kobe, Japan
90475
904752 = 13932 + 13942 + 13952 + ... + 30092.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by Yoshio Mimura, Kobe, Japan
90542
905422± 3 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by Yoshio Mimura, Kobe, Japan
90546
905462± 5 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by Yoshio Mimura, Kobe, Japan
90594
905942± 5 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by Yoshio Mimura, Kobe, Japan
90601
90601 = 3012, a zigzag square.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by 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).
by Yoshio Mimura, Kobe, Japan
90625
906252 = 8212890625.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by Yoshio Mimura, Kobe, Japan
90668
906682 = 8220686224, a square with even digits.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by 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).
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, 2014by Yoshio Mimura, Kobe, Japan
90729
907292 = (372 + 8)(24452 + 8).
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by 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, 2014by 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).
by Yoshio Mimura, Kobe, Japan
90752
907522± 3 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by 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, 2014by Yoshio Mimura, Kobe, Japan
90783
907832± 2 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by Yoshio Mimura, Kobe, Japan
90794
907942± 3 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by 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).
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).
by Yoshio Mimura, Kobe, Japan
90884
908842± 3 are primes.
Page of Squares : First Upload April 13, 2014 ; Last Revised April 13, 2014by Yoshio Mimura, Kobe, Japan
90898
908982 = 8262446404, a square with even digits.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by Yoshio Mimura, Kobe, Japan
90908
909082 = 8264264464, a square with even digits.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by 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, 2014by Yoshio Mimura, Kobe, Japan
90932
909322 = 8268628624, a square with even digits.
Page of Squares : First Upload December 15, 2012 ; Last Revised December 15, 2012by Yoshio Mimura, Kobe, Japan