   Chapter 2.3, Problem 19E

Chapter
Section
Textbook Problem

If a ,   b ,   c ,   m and n are integers with a | b and a | c . Prove that a | ( m b + n c ) .

To determine

To prove: a|(mb+nc) if a,b,c,m and n are integers with a|b and a|c.

Explanation

Given information:

Let a,b,c,m and n are integers such that a|b and a|c.

Formula used:

Divisor:

Let a,b be any integers, a is divisor of b, write as a|b if there is an integer c such that b=ac.

Proof:

Let a,b,c,m and n are integers such that a|b and a|c.

Then, there exist an integer x and y such that,

b=ax and c=ay

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