Compatibility of equations with truncated Newton's binomials

TL;DR

This paper investigates the conditions under which equations involving truncated Newton's binomials are solvable in integers, focusing on divisibility criteria related to binomial exponents and parameters.

Contribution

It introduces specific divisibility conditions that determine the solvability of equations with truncated Newton's binomials, expanding understanding of their integer solutions.

Findings

Resolvability depends on divisibility of binomials by characteristic parameters.

Conditions are specified for equations with two and three integer binomials.

Divisibility by binomial exponents is key to solution existence.

Abstract

The resolvability of equations in integers containing truncated Newton's binomial, is determined by the divisibility of the binomial by the characteristic parameters of the equation, which most often is the binomial exponent. Two types of equations containing binomials from two and three integers are investigated. Conditions of resolvability of the equations are specified based on the characteristics of their parameters.