Give a counterexample to show that the statement of exercise 33 is false if the hypothesis that gcd(a,b)=1 removed.

To find:

A counter example of the result “prove that for all integers a,b and c, if gcd(a,b)=1 and a|c and b|c then ab|c ”.

Given information:

a,b,c are integers

gcd(a,b)=1

Concept used:

gcd: Greatest common divisor

Calculation:

The objective is to give a counter example of the result “prove that for all integers a,b and c, if gcd(a,b)=1 and a|c and b|c then ab|c ”.

Counterexample.

Let a=2, b=4 and c=16

Then, a|c becomes ac=216 since 16=2×8.

Similarly, b|c becomes bc=416 since 16=4×4