   Chapter 2.4, Problem 8E

Chapter
Section
Textbook Problem

If a = b c + 1 , prove ( a ,   b ) = 1 .

To determine

To prove: If a=bc+1, then (a,b)=1.

Explanation

Given information:

a=bc+1

Formula used:

Greatest Common Divisors:

Let a and b be the integers, at least one of them is non-zero. Then, there exists a unique greatest common divisor d of a and b. Moreover, d can be written as d=am+bn for integers m and n, and d is the smallest positive integer that can be written in this form.

Proof:

Let a=bc+1,

This can written as abc=1

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