Ternary cyclotomic polynomials with an optimally large set of coefficients

Ternary cyclotomic polynomials are polynomials of the form , where are odd primes and the product is taken over all primitive -th roots of unity . We show that for every there exists an infinite family of polynomials such that the set of coefficients of each of these polynomials coincides with the set of integers in the interval . It is known that no larger range is possible even if gaps in the range are permitted.