Quotient polynomials with positive coefficients

TL;DR

This paper establishes the precise conditions under which the quotient and remainder in polynomial division have exclusively positive coefficients, providing a complete characterization.

Contribution

It offers an optimal necessary and sufficient condition for quotient and remainder polynomials to have positive coefficients in polynomial division.

Findings

Derived an exact criterion for positivity of quotient coefficients

Characterized conditions for positive remainder coefficients

Enhanced understanding of polynomial division with positive constraints

Abstract

We give an optimal necessary and sufficient condition for the quotient polynomial and remainder in the division algorithm to have positive coefficients.