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 Post subject: questionPosted: Sun, 12 Nov 2006 02:02:37 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 21 May 2003 10:00:57 UTC
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Location: Australia
Let n be a positive integer, let a_0 = 1, and suppose that for every positive integer i the number a_i is the residue modulo n of (a_i-1)^2 - 1. Suppose that p is a prime divisor of n.

(a) Show that there exist integers i and j such that 0 <= i < j < p such that a_i = a_j (mod p).

(b) Show that if a_i = a_j (mod p) then a_i+k = a_j+k (mod p) for all positive integers k.

(c) Let i and j be as in (a), and suppose that k is a multiple of j - i with i <= k < j. Show that a_2k = a_k (mod p).

I cannot do (a), but can do part (b) and (c) assuming (a)...

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 Post subject: Posted: Sun, 29 Jul 2007 03:34:46 UTC
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Joined: Tue, 6 Feb 2007 15:49:02 UTC
Posts: 2594
What if p = 2?

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