Strayer Elementary Number Theory 1. 3. 47a.

 

Note the author asked for a non-negative m, but I changed this. It is not always true. For example, let m=0, let a=9, let b=3. Then (a^(m),b)=(9^(0),3)=(1,3)=1 does NOT imply that (a,b)=(9,3)=1, because of course (9,3)=3.

EDIT: Note typo at the beginning of the induction step... it should be that m is an element of {2,3,...,n-1}.