A proof of the Corrected Beiter conjecture
Abstract
We say that a cyclotomic polynomial n(x) has order three if n is the product of three distinct primes, p<q<r. Let A(n) be the largest absolute value of a coefficient of n(x) and M(p) be the maximum of A(pqr). In 1968, Sister Marion Beiter conjectured that A(pqr)<=(p+1)/2. In 2008, Yves Gallot and Pieter Moree showed that the conjecture is false for every p>=11, and they proposed the Corrected Beiter conjecture: A(pqr)<=2p/3. Here we will give a proof of this conjecture.
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