Diophantine equations in Number Theory

Here is the problem:

If a and b are relatively prime positive integers, prove that the
Diophantine equation ax-by = c has infinitely many solutions in the
positive integers.

[Hint: There exist integers x0 and y0 such that ax0+by0 = c. For any
integer t, which is larger that both |x0|/b and |y0|/a, a positive
solution of the given equation is x = x0+bt, y = -(y0-at).]

(Note: x0 is x null or naught...I didn't know how else to write it.)

I'm stuck on this homework problem. If anyone can please help me I
would greatly appreciate it. Thank you.