Ways to prove the Zsigmondy's theorem

Question

How to prove the Zsigmondy's Theorem with cyclotomic polynomials? Is there a proof which does not rely on cyclotomic polynomials? How many ways are there?

Related: Elementary proof of Zsigmondy's theorem – Bart Michels Apr 11 '15 at 10:57 — Bart Michels, Apr 11 '15 at 10:57

Dietrich Burde · Accepted Answer · 2013-10-07T18:10:19.063

5

There are several proofs available for Zsigmondy's theorem: Zsigmondy (1892), Birkhoff and Vandiver (1904), Dickson (1905), Artin (1955), Hering (1974) and Lüneburg (1981). All of them use cyclotomic polynomials (which is natural). If there is some proof without it, it might be just artificial.
A reference for a proof is (among many other sources) the article "On Zsigmondy primes" by M. Roitman (‎1997).

edited Oct 07 '13 at 18:10

answered Oct 07 '13 at 17:31

Dietrich Burde

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Ways to prove the Zsigmondy's theorem

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