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 Divisibility (Posted on 2007-01-08)
Let A be an integer, P an odd prime and n=3 be the smallest integer for which A^n - 1 is divisible by P.
Determine the smallest integer m for which (A+1)^m - 1 is divisible by P.

 No Solution Yet Submitted by atheron No Rating

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 re: some thoughts | Comment 5 of 6 |
(In reply to some thoughts by Dennis)

I have also showed to myself that (A+1)^m-1, where 1¡Âm¡Ã5, does not possess the factor (A©÷+2A+1), but since (A©÷+2A+1) is not necessarily prime, I am unable to show that (A+1)^m-1, where 1¡Âm¡Ã5, never posess the factor p.

Are you able to show that m=6 is the smallest integer even if A is really big?

 Posted by David Johnson on 2007-01-21 03:30:38

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