Zsigmondy's theorem
From Wikipedia, the free encyclopedia
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
- K. Zsigmondy (1892). "Zur Theorie der Potenzreste". Journal Monatshefte für Mathematik 3 (1): 265–284. doi:.
- Th. Schmid (1927). "Karl Zsigmondy". Jahresbericht der Deutschen Mathematiker-Vereinigung 36: 167–168.
- Moshe Roitman (1997). "On Zsigmondy Primes". Proceedings of the American Mathematical Society 125 (7): 1913–1919. doi:.
- Walter Feit (1988). "On Large Zsigmondy Primes". Proceedings of the American Mathematical Society 102 (1): 29–36. doi:.

