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Divisibility (Posted on 2007-01-08) Difficulty: 3 of 5
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    
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Question re: some thoughts | Comment 5 of 6 |
(In reply to some thoughts by Dennis)

I agree with you that M=6 is the answer. P divides (A+2A+1) and (A+1)^6-1 = A(A+2)(A+3A+3)(A+A+1)

I have also showed to myself that (A+1)^m-1, where 1m5, 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 1m5, 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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