I m stuck on a decade old olympiad problem which is as follow:
Find least possible value of a+b where a,b are positive integers such that 11 divides a+13b and 13 divides a+11b.
I m clueless. I tried something like a+11b=13k and a+13b=11m (for some positive integer k and m), but that didn't work.
Hoping for help,I shall be thankful if you give an easy answer with a bit of explaination.