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Show that if a|m and a|(ms+nt) for some integers a≠0, m, s, n, and t, then a|nt.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 24E: Let (a,b)=1. Prove that (a,bn)=1 for all positive integers n.

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Show that if a|m and a|(ms+nt) for some integers a≠0, m, s, n, and t, then a|nt.

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