If (2^a -1) divides (2^{a(b-1)} + 2^{a(b-2)} + ... + 2^2a + 2^a + 1) for a, b 2^a - 1 and 2^b -1 being odd primes What does it tell us about b?

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Originally Posted by helgamauer If (2^a -1) divides (2^{a(b-1)} + 2^{a(b-2)} + ... + 2^2a + 2^a + 1) for a, b 2^a - 1 and 2^b -1 being odd primes What does it tell us about b? It would imply that . Note that for any positive integer . Therefore, . Thus divides , and since is prime we must have . By the way, .