IIT JEE , AIEEE Forum - Mathematics , Algebra

abhirup_ab

If a and b are natural numbers such that a + 13b is divisible by 11 and a + 11b is divisible by 13, find the minimum value of a and b

hsbhatt

There was a similar question earlier which asked to minimise a+b and I take it that you too intended the same

We have, $a+13b \equiv 0 \bmod 11 \Rightarrow a+2b \equiv 0 \bmod 11$

Similarly $a+11b \equiv 0 \bmod 13 \Rightarrow a-2b \equiv 0 \bmod 13$

Thus a+2b is divisible by 11 and a-2b is divisible by 13.

Looks to me that a = 23 and b =5 gives the minimum for a+b = 28.

pramod6990