Thread: Finding number of integers not satisfying an expression

Hi,
For any a, b >= 0, how can one find the number of positive integers which cannot be expressed as ax + by where gcd(x,y) = 1 and x,y > 1
E.g for x,y = 3,4 the number of such integers is 3
I think that extended euledian algorithm can be used here but am not sure how.
Thanks.

Given coprime positive integers x, y, the set of positive integers that cannot be represented as ax + by for some nonnegative integers a, b is called the set of gaps of a numerical semigroup with two generators x and y. The number of elements in the set of gaps is called the genus of the semigroup. In the case of two generators x and y, the genus equals (x − 1)(y − 1) / 2.

thanks a lot emakarov