Zsigmondy's theorem

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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 k < n, with the following exceptions:

  • a = 2, b = 1, and n = 6; or
  • a + b is a power of two, and n = 2.

[edit] History

The theorem was discovered by Karl Zsigmondy working in Vienna from 1894 til 1925.

[edit] References