相邻的三元分圆系数最多相差1
Neighboring ternary cyclotomic coefficients differ by at most one
摘要：
一个分圆多项式Phi_n（x）称为三元多项式，如果n=pqr，其中p，q和r是不同的奇素因子.三元分圆多项式是最简单的多项式，其系数的行为尚未完全理解。Eli Leher在2007年证明了相邻的三元分圆系数最多相差4。我们表明，事实上，他们最多相差一个。因此，出现在三元分圆多项式中的系数集合由连续整数组成。作为应用，我们以一种更简单的方式重新证明了Bachman在2004年关于具有最优大系数集的三元分圆多项式的一个结果.
英文摘要：
A cyclotomic polynomial Phi_n(x) is said to be ternary if n=pqr with p,q and r distinct odd prime factors. Ternary cyclotomic polynomials are the simplest ones for which the behaviour of the coefficients is not completely understood. Eli Leher showed in 2007 that neighboring ternary cyclotomic coefficients differ by at most four. We show that, in fact, they differ by at most one. Consequently, the set of coefficients occurring in a ternary cyclotomic polynomial consists of consecutive integers. As an application we reprove in a simpler way a result of Bachman from 2004 on ternary cyclotomic polynomials with an optimally large set of coefficients.
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