On the coefficients of the Cyclotomic polynomial

For n < 105 all coefficients of F,(X) are zb 1 or 0. For n = 105, the coefficient 2 occurs for the first time. Denote by A, the greatest coefficient of F,,(x) (in absolute value). Schur proved that lim sup A ,, = 00. Emma Lehmerl proved that A fi >cn l/a for infinitely many 72, In fact she proved that infinitely many such n’s are of the form Pqr with p, q, and r prime. In the present note we are going to prove that A,>nb for every K and infinitely many n. This is implied by the still sharper theorem: