32009
320092 = 1024576081, and 1024 = 322, 576081 = 7592.
Page of Squares : First Upload May 26, 2012 ; Last Revised May 26, 2012by Yoshio Mimura, Kobe, Japan
32010
320102 = (182 + 6)(242 + 6)(732 + 6) = (32 + 6)(42 + 6)(242 + 6)(732 + 6).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32041
32041 = 1792 is a square with different digits.
Page of Squares : First Upload May 26, 2012 ; Last Revised May 26, 2012by Yoshio Mimura, Kobe, Japan
32043
320432 = 1026753849 is a square with different digits.
Page of Squares : First Upload May 26, 2012 ; Last Revised May 26, 2012by Yoshio Mimura, Kobe, Japan
32045
320452 = (122 + 1)(382 + 1)(702 + 1)
= (32 + 4)(52 + 4)(92 + 4)(1792 + 4) = (22 + 9)(42 + 9)(222 + 9)(802 + 9).
by Yoshio Mimura, Kobe, Japan
32046
320462 = (22 + 3)(122 + 3)(9992 + 3) = (42 + 5)(392 + 5)(1792 + 5).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32056
320562± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32076
320762 = (22 + 2)(32 + 2)(42 + 2)(52 + 2)(82 + 2)(222 + 2) = (22 + 2)(42 + 2)(222 + 2)(1402 + 2)
= (22 + 2)(52 + 2)(82 + 2)(142 + 2)(222 + 2).
453 + 32076 = 3512, 453 - 32076 = 2432.
Page of Squares : First Upload May 26, 2012 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32095
320952 = 12112 + 12132 + 12152 + 12172 + ... + 19952.
Page of Squares : First Upload May 26, 2012 ; Last Revised May 26, 2012by Yoshio Mimura, Kobe, Japan
32102
321022± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32110
321102± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32116
321162 = (22 + 3)(52 + 3)(112 + 3)(2062 + 3).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32142
321422± 5 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32145
The quadratic polynomial 32145X2 - 170730X + 265321 takes the values 3562, 2292, 2062, 3112, 4642, 6312 at X = 1, 2,..., 6,
Page of Squares : First Upload June 2, 2012 ; Last Revised June 2, 2012by Yoshio Mimura, Kobe, Japan
32178
321782± 5 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32229
322292± 2 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32256
2602 + 32256 = 3162, 2602 - 32256 = 1882.
322562 = (152 - 1)(172 - 1)(1272 - 1) = (22 - 1)(32 - 1)(52 - 1)(72 - 1)(132 - 1)(152 - 1)
= (32 - 1)(72 - 1)(132 - 1)(1272 - 1) = (32 - 1)(72 - 1)(172 - 1)(972 - 1).
by Yoshio Mimura, Kobe, Japan
32274
322742 = (52 + 2)(182 + 2)(3442 + 2).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32286
322862 = 1042385796 is a square with different digits.
Page of Squares : First Upload May 26, 2012 ; Last Revised May 26, 2012by Yoshio Mimura, Kobe, Japan
32298
322982 = (12 + 5)(32 + 5)(35242 + 5).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32340
323402 = (12 + 6)(22 + 6)(42 + 6)(62 + 6)(82 + 6)(152 + 6)
= (12 + 6)(42 + 6)(62 + 6)(182 + 6)(222 + 6) = (12 + 6)(42 + 6)(62 + 6)(82 + 6)(482 + 6)
= (22 + 6)(42 + 6)(182 + 6)(1202 + 6) = (22 + 6)(42 + 6)(62 + 6)(152 + 6)(222 + 6)
= (42 + 6)(62 + 6)(222 + 6)(482 + 6).
by Yoshio Mimura, Kobe, Japan
32362
323622± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32384
323842 = (12 + 7)(22 + 7)(32 + 7)(132 + 7)(652 + 7)
= (12 + 7)(22 + 7)(32 + 7)(42 + 7)(92 + 7)(192 + 7) = (12 + 7)(22 + 7)(52 + 7)(92 + 7)(652 + 7)
= (12 + 7)(22 + 7)(532 + 7)(652 + 7) = (12 + 7)(32 + 7)(42 + 7)(192 + 7)(312 + 7)
= (12 + 7)(42 + 7)(92 + 7)(132 + 7)(192 + 7) = (12 + 7)(42 + 7)(112 + 7)(2112 + 7)
= (12 + 7)(52 + 7)(312 + 7)(652 + 7) = (22 + 7)(42 + 7)(52 + 7)(132 + 7)(272 + 7)
= (22 + 7)(42 + 7)(92 + 7)(112 + 7)(192 + 7) = (22 + 7)(42 + 7)(272 + 7)(752 + 7)
= (22 + 7)(112 + 7)(132 + 7)(652 + 7) = (32 + 7)(92 + 7)(132 + 7)(652 + 7)
= (42 + 7)(112 + 7)(192 + 7)(312 + 7) = (52 + 7)(272 + 7)(2112 + 7) = (92 + 7)(532 + 7)(652 + 7).
by Yoshio Mimura, Kobe, Japan
32400
324002 = (22 - 1)(42 - 1)(112 - 1)(172 - 1)(262 - 1) = (42 - 1)(172 - 1)(192 - 1)(262 - 1).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32397
323972± 2 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32412
324122 = (172 + 3)(212 + 3)(902 + 3).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32451
324512± 2 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32472
324722 = (162 + 8)(192 + 8)(1042 + 8) = (192 + 8)(282 + 8)(602 + 8)
= (42 + 8)(52 + 8)(192 + 8)(602 + 8).
by Yoshio Mimura, Kobe, Japan
32487
324872± 2 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32500
325002 = 2232 + 2242 + 2252 + ... + 14702.
325002 = (12 + 1)(22 + 1)(32 + 1)(72 + 1)(82 + 1)(572 + 1) = (12 + 1)(32 + 1)(72 + 1)(182 + 1)(572 + 1).
Page of Squares : First Upload May 26, 2012 ; Last Revised November 9, 2013by Yoshio Mimura, Kobe, Japan
32502
325022± 5 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32508
325082 = (12 + 5)(32 + 5)(72 + 5)(92 + 5)(522 + 5) = (12 + 5)(32 + 5)(92 + 5)(112 + 5)(342 + 5).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32550
325502 = (12 + 6)(22 + 6)(52 + 6)(122 + 6)(572 + 6) = (12 + 6)(32 + 6)(52 + 6)(62 + 6)(882 + 6)
= (12 + 6)(32 + 6)(362 + 6)(882 + 6) = (22 + 6)(32 + 6)(52 + 6)(82 + 6)(572 + 6)
= (22 + 6)(32 + 6)(52 + 6)(132 + 6)(362 + 6) = (22 + 6)(32 + 6)(272 + 6)(982 + 6)
= (32 + 6)(62 + 6)(132 + 6)(982 + 6) = (52 + 6)(82 + 6)(122 + 6)(572 + 6)
= (52 + 6)(122 + 6)(132 + 6)(362 + 6) = (52 + 6)(362 + 6)(1622 + 6) = (62 + 6)(572 + 6)(882 + 6)
= (122 + 6)(272 + 6)(982 + 6).
by Yoshio Mimura, Kobe, Japan
32560
325602± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32562
325622 = (12 + 2)(42 + 2)(202 + 2)(2212 + 2).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32578
325782± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32592
325922± 5 are primes.
325922 = (22 - 1)(188172 - 1).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32640
326402 = (72 - 1)(92 - 1)(162 - 1)(332 - 1).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32666
326662± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32732
327322± 3 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32760
327602 = (22 - 1)(32 - 1)(42 - 1)(272 - 1)(642 - 1) = (22 - 1)(42 - 1)(132 - 1)(142 - 1)(272 - 1)
= (22 - 1)(42 - 1)(272 - 1)(1812 - 1) = (22 - 1)(112 - 1)(272 - 1)(642 - 1) = (22 - 1)(272 - 1)(7012 - 1)
= (32 - 1)(42 - 1)(82 - 1)(142 - 1)(272 - 1) = (32 - 1)(132 - 1)(142 - 1)(642 - 1)
= (32 - 1)(642 - 1)(1812 - 1) = (42 - 1)(52 - 1)(272 - 1)(642 - 1) = (42 - 1)(62 - 1)(272 - 1)(532 - 1)
= (82 - 1)(112 - 1)(142 - 1)(272 - 1) = (132 - 1)(142 - 1)(1812 - 1) = (192 - 1)(272 - 1)(642 - 1).
by Yoshio Mimura, Kobe, Japan
32761
32761 = 1812 is a square with different digits.
Page of Squares : First Upload May 26, 2012 ; Last Revised May 26, 2012by Yoshio Mimura, Kobe, Japan
32768
327682 = (12 + 7)(52 + 7)(112 + 7)(1812 + 7).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32770
327702± 3 are primes.
327702 = (12 + 1)(122 + 1)(152 + 1)(1282 + 1) = (152 + 1)(172 + 1)(1282 + 1).
Page of Squares : First Upload November 9, 2013 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32788
327882 = 2986 x 2987 + 2988 x 2989 + 2990 x 2991 + 2992 x 2993 + ... + 3208 x 3209.
Page of Squares : First Upload May 26, 2012 ; Last Revised May 26, 2012by Yoshio Mimura, Kobe, Japan
32800
328002 = (12 + 4)(22 + 4)(42 + 4)(182 + 4)(642 + 4) = (42 + 4)(62 + 4)(182 + 4)(642 + 4).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32824
328242 = (22 + 7)(92 + 7)(10552 + 7) = (312 + 7)(10552 + 7).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32832
328322 = (42 + 8)(82 + 8)(122 + 8)(642 + 8).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32850
328502 = (42 + 9)(82 + 9)(92 + 9)(812 + 9).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32856
1852 + 32856 = 2592, 1852 - 32856 = 372.
Page of Squares : First Upload May 26, 2012 ; Last Revised May 26, 2012by Yoshio Mimura, Kobe, Japan
32868
328682 = (12 + 5)(22 + 5)(32 + 5)(162 + 5)(742 + 5) = (12 + 5)(22 + 5)(42 + 5)(132 + 5)(742 + 5)
= (12 + 5)(22 + 5)(162 + 5)(2772 + 5) = (12 + 5)(112 + 5)(162 + 5)(742 + 5)
= (22 + 5)(42 + 5)(112 + 5)(132 + 5)(162 + 5) = (22 + 5)(112 + 5)(132 + 5)(742 + 5)
= (32 + 5)(72 + 5)(162 + 5)(742 + 5) = (42 + 5)(72 + 5)(132 + 5)(742 + 5)
= (42 + 5)(712 + 5)(1012 + 5) = (52 + 8)(182 + 8)(3142 + 8) = (72 + 5)(162 + 5)(2772 + 5).
by Yoshio Mimura, Kobe, Japan
32922
329222± 5 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32928
329282 = (12 + 3)(22 + 3)(32 + 3)(52 + 3)(92 + 3)(372 + 3).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32943
329432± 2 are primes.
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan
32964
329642 = (22 + 8)(222 + 8)(4292 + 8).
Page of Squares : First Upload February 19, 2014 ; Last Revised February 19, 2014by Yoshio Mimura, Kobe, Japan