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,

## Sunday, January 6, 2008

### More number theory

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