Re: [math-fun] n and n^3 have all digits odd
Quoth rcs@xmission.com
Cubes (mod 9) are always 0, 1, or 8. The low order ternary digits are 00, 01, or 22. --Rich
To settle the decimal case, you have to go up to mod 10^9 at which point you will discover that none of the 1000 possibilities is all odd digits. I did it by grepping the output of this program: #include <stdio.h> int main(){ for(int i=0;i!=1000;i++) printf("%09d\n", i*i*i); return 0; } -- Tom Duff. Seize you your paper and go into an art seminar!
I'm not sure I understand; 111113519 ** 3 = 1371831295485468999177359 The last nine digits of that are all odd. Put another one on the front of the left hand side and you get a value on the right hand side with the last ten digits all odd. Not sure why this can't keep going . . . On Thu, Apr 19, 2012 at 2:34 PM, Tom Duff <td@pixar.com> wrote:
To settle the decimal case, you have to go up to mod 10^9 at which point you will discover that none of the 1000 possibilities is all odd digits.
I did it by grepping the output of this program:
#include <stdio.h> int main(){ for(int i=0;i!=1000;i++) printf("%09d\n", i*i*i); return 0; }
-- Tom Duff. Seize you your paper and go into an art seminar!
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-- -- http://cube20.org/ -- http://golly.sf.net/ --
[1,11,119,1135,11151,111151,1111537,11111579,111113519,1111113519,11111137751,111111137751,1111111137751, 11111111137751,111111111319719,1111111115771999,11111111117157551,111111111133139353,1111111111333797337] On Thu, Apr 19, 2012 at 5:37 PM, Tom Rokicki <rokicki@gmail.com> wrote:
I'm not sure I understand;
111113519 ** 3 = 1371831295485468999177359
The last nine digits of that are all odd.
Put another one on the front of the left hand side and you get a value on the right hand side with the last ten digits all odd.
Not sure why this can't keep going . . .
On Thu, Apr 19, 2012 at 2:34 PM, Tom Duff <td@pixar.com> wrote:
To settle the decimal case, you have to go up to mod 10^9 at which point you will discover that none of the 1000 possibilities is all odd digits.
I did it by grepping the output of this program:
#include <stdio.h> int main(){ for(int i=0;i!=1000;i++) printf("%09d\n", i*i*i); return 0; }
-- Tom Duff. Seize you your paper and go into an art seminar!
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-- -- http://cube20.org/ -- http://golly.sf.net/ --
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participants (3)
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Tom Duff -
Tom Rokicki -
Victor Miller