# The Midterm Coefficient of the Cyclotomic Polynomial F pq (x)

@article{Beiter1964TheMC,
title={The Midterm Coefficient of the Cyclotomic Polynomial F pq (x)},
author={Marion Beiter},
journal={American Mathematical Monthly},
year={1964},
volume={71},
pages={769}
}
• M. Beiter
• Published 1 August 1964
• Mathematics
• American Mathematical Monthly
A Survey on Coefficients of Cyclotomic Polynomials
Cyclotomic polynomials play an important role in several areas of mathematics and their study has a very long history, which goes back at least to Gauss (1801). In particular, the properties of their
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On Arithmetic Progressions of Powers in Cyclotomic Polynomials
• H. Chu
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• 2021
The necessary conditions for when powers corresponding to positive/negative coefficients of are in arithmetic progression are determined and the result when n = pq is generalized to the so-called inclusion-exclusion polynomials first introduced by Bachman.
On the Scaled Inverse of $(x^i-x^j)$ modulo Cyclotomic Polynomial of the form $\Phi_{p^s}(x)$ or $\Phi_{p^s q^t}(x)$
• Mathematics
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Abstract. The scaled inverse of a nonzero element a(x) ∈ Z[x]/f(x), where f(x) is an irreducible polynomial over Z, is the element b(x) ∈ Z[x]/f(x) such that a(x)b(x) = c (mod f(x)) for the smallest
Representation of $\frac{1}{2}(F_n-1)(F_{n+1}-1)$ and $\frac{1}{2}(F_n-1)(F_{n+2}-1)$
Let $a, b\in \mathbb{N}$ be relatively prime. We consider $(a-1)(b-1)/2$, which arises in the study of the $pq$-th cyclotomic polynomial, where $p,q$ are distinct primes. We prove two possible
Explicit expression for a family of ternary cyclotomic polynomials
• Mathematics
• 2018
In this paper, we give an explicit expression for a certain family of ternary cyclotomic polynomials: specifically $\Phi_{p_{1}p_{2}p_{3}}$, where $p_{1}<p_{2}<p_{3}$ are odd primes such that \$p_{2}
Numerical Semigroups, Cyclotomic Polynomials, and Bernoulli Numbers
• P. Moree
• Mathematics, Computer Science
Am. Math. Mon.
• 2014
The intent of this paper is to better unify the various results within the cyclotomic polynomial and numerical semigroup communities.
Constants of cyclotomic derivations
• Mathematics
• 2013
Let k[X]=k[x0,…,xn−1] and k[Y]=k[y0,…,yn−1] be the polynomial rings in n⩾3 variables over a field k of characteristic zero containing the n-th roots of unity. Let d be the cyclotomic derivation of

## References

Introduction to Number Theory
• Mathematics
• 1966
A specific feature of this text on number theory is the rather extensive treatment of Diophantine equations of second or higher degree. A large number of non-routine problems are given. The book is