Abstract
Let a n ( k ) be the coefficient of t k in the nth cyclotomic polynomial Φ n ( t ) = ∏ j = 1 gcd ( j , n ) = 1 n ( t − e 2 π j i n ) . Let M ( k ) = lim x → ∞ 1 x ∑ n ⩽ x a n ( k ) be the average of a n ( k ) , as introduced by Möller, and let f k = π 2 6 M ( k ) k ∏ q ⩽ k q prime ( q + 1 ) . It was asked by Y. Gallot, P. Moree and H. Hommersom if the f k are integers for all k. In this paper, we prove that this is so. We further show that for any fixed natural number N, f k contains N as a factor for sufficiently large k.
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