All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 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

Comments: ( Back to comment list | You must be logged in to post comments.)
 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 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

 Search: Search body:
Forums (1)