Consider a,b N* when a > b. Show that if a mod b 0, then gcd(a,b) (Greatest Common Denominator) divides (a mod b).

One way to prove this assumption is to write a = kb + r for r,k N* and r < b, from the definition of the euclidian division. We can also consider the hypothesis a >b and y = gcd(a,b). Then, we can conclude the proof by showing that y divides r because a = sy and b = ty for s,t N* by definition of gcd. Please prove definitions and proprieties of modular arithmetic if used to answer this question.