More number theory

Number theory is my favorite, and most of these problems are about numbers.Here`s another one:
if 11 divides (a+13*b) and 13 divides (a+11*b)
what is the least value of (a+b)?
This one`s easy, so here`s solution:
a+13b=11r =>a+2b=11p, where p=r-b
a+11b=13s =>a-2b=13q, where q=s-b
2a=11p+13q,
4b=11p-13q, thus p>q.
The least solution is: p=3 and q=1, a=23 and b=5, a+b=28,