Fight for Attendence

Prof. R.K.Vats of NIT Hamirpur has given a problem to the whole class and has imposed a condition that he won't give attendance to those who don't solve it within time. He gave the equation , ax+by=c where a, b, c are three positive integers. The problem is to determine if there exists at least one solution for some integral value of x and y where x, y can be negative or non-negative integers.