Which of the following is the condition for ax+by=cax + by = cax+by=c to have a solution where x,y>0x, y > 0x,y>0?
gcd(a,b)∣c\text{gcd}(a, b) | cgcd(a,b)∣c and c>abc > abc>ab
gcd(a,b)∣c\text{gcd}(a, b) | cgcd(a,b)∣c and c≥a+bc \ge a+bc≥a+b
gcd(a,b)∣c\text{gcd}(a, b) | cgcd(a,b)∣c and c>abgcd(a,b)c > \frac{ab}{\text{gcd}(a,b)}c>gcd(a,b)ab
a,b∣ca, b | ca,b∣c