10000
100002 = (12 + 4)(42 + 4)(62 + 4)(112 + 4)(142 + 4).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10032
100322 = (122 + 8)(162 + 8)(502 + 8) = (42 + 8)(162 + 8)(1262 + 8)
= (62 + 8)(72 + 8)(122 + 8)(162 + 8).
by Yoshio Mimura, Kobe, Japan
10050
10050, 10051, 10052 and 10053 are four consecutive integers having square factors (the 7th case).
Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
10080
100802 = (112 - 1)(132 - 1)(712 - 1) = (132 - 1)(192 - 1)(412 - 1) = (22 - 1)(112 - 1)(132 - 1)(412 - 1)
= (22 - 1)(132 - 1)(4492 - 1) = (22 - 1)(32 - 1)(292 - 1)(712 - 1)
= (22 - 1)(32 - 1)(42 - 1)(132 - 1)(412 - 1) = (22 - 1)(32 - 1)(42 - 1)(62 - 1)(72 - 1)(132 - 1)
= (22 - 1)(32 - 1)(52 - 1)(62 - 1)(712 - 1) = (22 - 1)(32 - 1)(52 - 1)(62 - 1)(82 - 1)(92 - 1)
= (22 - 1)(32 - 1)(82 - 1)(92 - 1)(292 - 1) = (22 - 1)(42 - 1)(62 - 1)(152 - 1)(172 - 1)
= (22 - 1)(52 - 1)(292 - 1)(412 - 1) = (22 - 1)(52 - 1)(62 - 1)(72 - 1)(292 - 1)
= (22 - 1)(62 - 1)(72 - 1)(112 - 1)(132 - 1) = (22 - 1)(82 - 1)(152 - 1)(492 - 1)
= (32 - 1)(42 - 1)(132 - 1)(712 - 1) = (32 - 1)(42 - 1)(82 - 1)(92 - 1)(132 - 1)
= (32 - 1)(62 - 1)(112 - 1)(552 - 1) = (32 - 1)(62 - 1)(72 - 1)(82 - 1)(112 - 1)
= (32 - 1)(82 - 1)(112 - 1)(412 - 1) = (32 - 1)(82 - 1)(4492 - 1) = (42 - 1)(52 - 1)(132 - 1)(412 - 1)
= (42 - 1)(52 - 1)(62 - 1)(72 - 1)(132 - 1) = (42 - 1)(72 - 1)(132 - 1)(292 - 1)
= (52 - 1)(292 - 1)(712 - 1) = (52 - 1)(82 - 1)(92 - 1)(292 - 1) = (62 - 1)(312 - 1)(552 - 1)
= (62 - 1)(72 - 1)(132 - 1)(192 - 1) = (62 - 1)(72 - 1)(82 - 1)(312 - 1) = (82 - 1)(312 - 1)(412 - 1)
= (82 - 1)(92 - 1)(112 - 1)(132 - 1).
1062 + 10080 = 1462, 1062 - 10080 = 342.
Page of Squares : First Upload March 10, 2012 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10081
100812 = (32 + 8)(24452 + 8).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10086
100862± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10098
100982 = (12 + 2)(102 + 2)(142 + 2)(412 + 2) = (12 + 2)(22 + 2)(412 + 2)(582 + 2)
= (12 + 2)(22 + 2)(52 + 2)(192 + 2)(242 + 2) = (12 + 2)(22 + 2)(72 + 2)(82 + 2)(412 + 2)
= (12 + 2)(32 + 2)(42 + 2)(102 + 2)(412 + 2) = (12 + 2)(32 + 2)(42 + 2)(72 + 2)(582 + 2)
= (12 + 2)(32 + 2)(52 + 2)(142 + 2)(242 + 2) = (12 + 2)(42 + 2)(72 + 2)(102 + 2)(192 + 2)
= (12 + 2)(72 + 2)(142 + 2)(582 + 2) = (192 + 2)(222 + 2)(242 + 2)
= (22 + 2)(32 + 2)(42 + 2)(72 + 2)(412 + 2) = (22 + 2)(72 + 2)(142 + 2)(412 + 2)
= (32 + 2)(52 + 2)(102 + 2)(582 + 2) = (32 + 2)(52 + 2)(72 + 2)(82 + 2)(102 + 2)
= (42 + 2)(412 + 2)(582 + 2) = (42 + 2)(52 + 2)(192 + 2)(242 + 2)
= (42 + 2)(72 + 2)(82 + 2)(412 + 2) = (72 + 2)(102 + 2)(1402 + 2).
by Yoshio Mimura, Kobe, Japan
10122
101222± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10143
101432 = (82 + 5)(322 + 5)(382 + 5).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10150
101502 = (132 + 6)(202 + 6)(382 + 6).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10162
101622 = 24 + 434 + 654 + 794 + 814.
Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011by Yoshio Mimura, Kobe, Japan
10192
101922 = (12 + 3)(72 + 3)(192 + 3)(372 + 3).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10206
102062 = (22 + 5)(42 + 5)(72 + 5)(1012 + 5).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10216
102162± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10230
102302 = (22 + 6)(32 + 6)(52 + 6)(1502 + 6) = (32 + 6)(52 + 6)(182 + 6)(262 + 6)
= (52 + 6)(122 + 6)(1502 + 6).
by Yoshio Mimura, Kobe, Japan
10262
102622± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10278
102782 = (22 + 2)(42 + 2)(9892 + 2).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10290
102902 = (12 + 6)(32 + 6)(82 + 6)(1202 + 6) = (12 + 6)(62 + 6)(222 + 6)(272 + 6)
= (22 + 6)(272 + 6)(1202 + 6) = (32 + 6)(222 + 6)(1202 + 6) = (62 + 6)(132 + 6)(1202 + 6).
by Yoshio Mimura, Kobe, Japan
10296
102962 = 1333 + 1343 + ... + 1643.
56 + 10296 = 1612, 56 - 10296 = 732.
Page of Squares : First Upload December 20, 2011 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
10304
103042 = (72 + 7)(212 + 7)(652 + 7).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10317
10317^2±± 2 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10368
103682± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10370
103702 = (12 + 1)(22 + 1)(42 + 1)(112 + 1)(722 + 1)
= (112 + 1)(132 + 1)(722 + 1) = (32 + 1)(42 + 1)(112 + 1)(722 + 1).
by Yoshio Mimura, Kobe, Japan
10374
103742± 5 are primes.
103742 = (12 + 3)(22 + 3)(42 + 3)(62 + 3)(722 + 3) = (32 + 3)(42 + 3)(62 + 3)(1102 + 3)
= (42 + 3)(332 + 3)(722 + 3) = (42 + 3)(52 + 3)(62 + 3)(722 + 3) = (62 + 3)(122 + 3)(1372 + 3)
= (62 + 3)(152 + 3)(1102 + 3) = (62 + 3)(232 + 3)(722 + 3).
by Yoshio Mimura, Kobe, Japan
10383
10383^2±± 2 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10384
103842± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10386
103862 = (22 + 2)(52 + 2)(8162 + 2).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10395
103952 = (22 - 1)(82 - 1)(102 - 1)(762 - 1) = (42 - 1)(82 - 1)(102 - 1)(342 - 1).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10400
104002 = (12 + 4)(22 + 4)(32 + 4)(42 + 4)(62 + 4)(162 + 4)
= (12 + 4)(22 + 4)(42 + 4)(102 + 4)(362 + 4) = (12 + 4)(42 + 4)(62 + 4)(102 + 4)(162 + 4)
= (22 + 4)(32 + 4)(42 + 4)(142 + 4)(162 + 4) = (22 + 4)(32 + 4)(42 + 4)(62 + 4)(362 + 4)
= (22 + 4)(62 + 4)(162 + 4)(362 + 4) = (42 + 4)(102 + 4)(142 + 4)(162 + 4)
= (42 + 4)(62 + 4)(102 + 4)(362 + 4).
by Yoshio Mimura, Kobe, Japan
10416
104162 = (12 + 3)(22 + 3)(32 + 3)(112 + 3)(512 + 3) = (12 + 3)(32 + 3)(112 + 3)(1352 + 3)
= (12 + 3)(92 + 3)(112 + 3)(512 + 3) = (32 + 3)(52 + 3)(112 + 3)(512 + 3).
by Yoshio Mimura, Kobe, Japan
10438
104382± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10452
104522 = (32 + 3)(62 + 3)(82 + 3)(592 + 3).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10458
104582 = (12 + 5)(22 + 5)(242 + 5)(592 + 5) = (72 + 5)(242 + 5)(592 + 5).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10464
104642± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10488
104882± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10492
104922 = (12 + 3)(132 + 3)(4002 + 3).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10504
105042 = (102 + 4)(10302 + 4) = (22 + 4)(32 + 4)(10302 + 4).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10506
105062± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10509
10509^2±± 2 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10530
105302 = (32 + 9)(62 + 9)(152 + 9)(242 + 9).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10544
105442 = 111175936, a square with odd digits except the last digit 6.
Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013by Yoshio Mimura, Kobe, Japan
10546
105462± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10560
105602 = (22 - 1)(32 - 1)(92 - 1)(2412 - 1) = (52 - 1)(92 - 1)(2412 - 1).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10584
1052 + 10584 = 1472, 1052 - 10584 = 212.
Page of Squares : First Upload March 10, 2012 ; Last Revised March 10, 2012by Yoshio Mimura, Kobe, Japan
10600
106002 = (12 + 4)(72 + 4)(142 + 4)(462 + 4) = (22 + 4)(72 + 4)(112 + 4)(462 + 4).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10614
106142 = (12 + 5)(422 + 5)(1032 + 5) = (132 + 5)(192 + 5)(422 + 5).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10616
106162± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10626
106262± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10646
106462 = 113337316, a square with odd digits except the last digit 6.
Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013by Yoshio Mimura, Kobe, Japan
10659
10659^2±± 2 are primes.
106592 = (32 + 8)(312 + 8)(832 + 8).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10660
106602 = (12 + 1)(22 + 1)(52 + 1)(92 + 1)(732 + 1) = (32 + 1)(52 + 1)(92 + 1)(732 + 1).
Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013by Yoshio Mimura, Kobe, Japan
10662
106622± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10664
106642 = (112 + 3)(132 + 3)(732 + 3).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10668
106682 = 333 * 334 * 335 + 335 * 336 * 337 + 337 * 338 * 339.
Page of Squares : First Upload October 26, 2103 ; Last Revised October 26, 2103by Yoshio Mimura, Kobe, Japan
10688
106882 = 114233344, 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, 2013by Yoshio Mimura, Kobe, Japan
10692
106922 = (12 + 2)(22 + 2)(32 + 2)(42 + 2)(82 + 2)(222 + 2)
= (12 + 2)(22 + 2)(42 + 2)(52 + 2)(82 + 2)(142 + 2) = (12 + 2)(22 + 2)(82 + 2)(142 + 2)(222 + 2)
= (12 + 8)(22 + 8)(52 + 8)(102 + 8)(172 + 8) = (22 + 2)(32 + 2)(42 + 2)(142 + 2)(222 + 2)
= (42 + 2)(82 + 2)(142 + 2)(222 + 2).
by Yoshio Mimura, Kobe, Japan
10695
106952 = 813 + 823 + ... + 1493.
Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011by Yoshio Mimura, Kobe, Japan
10730
107302 = (22 + 1)(412 + 1)(1172 + 1) = (62 + 1)(412 + 1)(432 + 1).
Page of Squares : First Upload November 9, 2013 ; Last Revised November 9, 2013by Yoshio Mimura, Kobe, Japan
10758
107582 = (12 + 2)(182 + 2)(3442 + 2).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10766
107662± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10772
107722± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10800
108002 = (22 - 1)(42 - 1)(72 - 1)(92 - 1)(262 - 1) = (22 - 1)(52 - 1)(262 - 1)(492 - 1).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10816
108162± 3 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10827
10827, 10828, 10829 and 10830 are four consecutive integers having square factors (the 8th case).
Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
10834
108342 = 117375556, a square with odd digits except the last digit 6.
Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013by Yoshio Mimura, Kobe, Japan
10850
108502 = (12 + 6)(22 + 6)(132 + 6)(982 + 6) = (12 + 6)(52 + 6)(82 + 6)(882 + 6)
= (52 + 6)(222 + 6)(882 + 6) = (82 + 6)(132 + 6)(982 + 6).
by Yoshio Mimura, Kobe, Japan
10854
108542 = (22 + 2)(202 + 2)(2212 + 2).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10878
108782 = (22 + 3)(122 + 3)(162 + 3)(212 + 3).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10914
109142 = 119115396, a square with odd digits except the last digit 6.
Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013by Yoshio Mimura, Kobe, Japan
10920
109202 = (142 - 1)(272 - 1)(292 - 1) = (22 - 1)(32 - 1)(62 - 1)(142 - 1)(272 - 1)
= (52 - 1)(62 - 1)(142 - 1)(272 - 1) = (82 - 1)(272 - 1)(512 - 1).
1092 + 10920 = 1512, 1092 - 10920 = 312,
1972 + 10920 = 2232, 1972 - 10920 = 1672.
by Yoshio Mimura, Kobe, Japan
10924
109242 = 119333776, a square with odd digits except the last digit 6.
10924, 10925, 10926, 10927 and 10928 are five consecutive integers having square factors (the 6th case).
Page of Squares : First Upload August 31, 2013 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
10944
109442 = 119771136, a square with odd digits except the last digit 6.
Page of Squares : First Upload August 31, 2013 ; Last Revised August 31, 2013by Yoshio Mimura, Kobe, Japan
10950
109502 = (12 + 9)(42 + 9)(82 + 9)(812 + 9).
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan
10962
109622± 5 are primes.
109622 = (12 + 5)(162 + 5)(2772 + 5) = (12 + 5)(32 + 5)(162 + 5)(742 + 5)
= (12 + 5)(42 + 5)(132 + 5)(742 + 5) = (112 + 5)(132 + 5)(742 + 5)
= (22 + 5)(132 + 5)(162 + 5)(172 + 5) = (22 + 5)(132 + 5)(2772 + 5)
= (22 + 5)(32 + 5)(132 + 5)(742 + 5) = (22 + 5)(32 + 5)(42 + 5)(132 + 5)(162 + 5)
= (22 + 5)(42 + 5)(112 + 5)(712 + 5) = (42 + 5)(112 + 5)(132 + 5)(162 + 5).
by Yoshio Mimura, Kobe, Japan
10978
109782 = 2! + 2! + 8! + 9! + 9! + 11! + 11! + 11!.
Page of Squares : First Upload December 20, 2011 ; Last Revised December 20, 2011by Yoshio Mimura, Kobe, Japan
10998
109982± 5 are primes.
Page of Squares : First Upload January 18, 2014 ; Last Revised January 18, 2014by Yoshio Mimura, Kobe, Japan