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To prove that as x cycles thru' the reduced residue set modulo m & y cycles thru' reduced residue set modulo n, nx + my cycles thru' reduced residue set modulo mn.

I am able to prove that:

a) nx1 + my1 [STRIKE]=[/STRIKE] nx2 + my2 and

b) nx + my is relatively prime to mn

But how do i prove that nx + my cycles thru' every one of the reduced residue set modulo mn without first proving that [tex]\phi[/tex][tex]\left(xy\right)\neq[/tex][tex]\phi\left(x\right)\phi\left(y\right)[/tex]