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- #1

- Apr 13, 2013

- 3,720

I have to show that if $(a,b)=1 \Rightarrow (a^m,b^n)=1$,without using primes!!!!

Suppose that $d=(a^m,b^n)$.Then $d|a^m , d|b^n$.

How can I continue?

Do I have to show that $(a^{m-1},d)=1$ and $(b^{n-1},d)=1$? If yes,how could I do this?