(10, k) Reversible Multiples

TL;DR

This paper investigates integers that become their reverse when multiplied by specific integers k, proving only k=1, 4, or 9 are possible and classifying such numbers accordingly.

Contribution

It establishes that only k=1, 4, or 9 can produce reverse multiples and provides a classification and general form for these integers.

Findings

k must be 1, 4, or 9 for reverse multiples

Classified reverse multiples into three categories

Derived the general form of these integers

Abstract

We consider the integers having the property of reversing when multiplied by a specific integer k. First, we proved that k should be either 1, 4 or 9. Second, we classify these integers as (10, 1)- reverse multiples, (10, 4)- reverse multiples and (10, 9)- reverse multiples. Then we conclude their general form.