Given that:
A + 13*B is divisible by 11 and:
A + 11*B is divisible by 13
whenever, each of A and B is a positive integer.

Determine the minimum value of A+B.

(In reply to A better answer by Tristan)

Correct. I should for completeness also have tried:

(a+13b) = 11m, (a+11b) = 13n, 0<b<a, (a+b)<78, which supplies:

{a = 23,   b = 5,   m = 8,   n = 6} with a+b=28 as a minimum.

Posted by broll on 2013-10-17 03:30:45