## 20 Citations

A Survey on Coefficients of Cyclotomic Polynomials

- Mathematics
- 2021

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…

J un 2 02 1 On the Scaled Inverse of ( x i − x j ) modulo Cyclotomic Polynomial of the form Φ p s ( x ) or Φ p s q t ( x )

- 2021

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…

On Arithmetic Progressions of Powers in Cyclotomic Polynomials

- Computer Science, MathematicsAm. Math. Mon.
- 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
- 2021

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 $\frac{1}{2}(F_n-1)(F_{n+2}-1)$

- Mathematics
- 2020

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

- Mathematics, Computer ScienceAm. 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…