Hello could anyone help me prove this Let ghk and n be integ

Hello, could anyone help me prove this:

Let g,h,k and n be integers with n > k > 1.If gcd(g,n)= k and there is an integer m such that gm h (mod n), then k divides h.

Aside from stating the assumtions I don\'t have a clue what to do next.

g,h, k and n are 4 integers.

gcd (g,n) = k implies that g and n are multiples of k

Let g = kl and n = ko

gm = h mod (n)

implies k(lm) = h mod n

As k is common factor in n also

k(lm) = h mod (k0)

This gives that k/h.