High Quality Content by WIKIPEDIA articles! In number theory, Zsigmondy's theorem states that if a > b > 0 are coprime integers, then for any natural number n > 1 there is a prime number p (called a primitive prime divisor) that divides an ? bn and does not divide ak ? bk for any positive integer k < n, with the following exceptions: a = 2, b = 1, and n = 6; or a + b is a power of two, and n = 2. This generalized Bang's theorem which states that if n>1 and n is not equal to 6, then 2n-1 has a prime divisor not dividing any 2k-1 with k<n.

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