I have two natural numbers M and N, M>N, and gcd(M, N) = 1. I want to find integers x and y such that

x*M + y*N = 1.

Can you give me x and y in terms of M and N; i.e., express x or y as a function of M and N.

Thanks,

HJin

gcd = greatest common divisor

For example,

gcd(4,8) = 4;
gcd(5, 16)=1.

Mathematics theory says that there exist x and y s.t.

x*M + y*N =1 if gcd(M, N)=1.

And I suspect that there are acutually infinitely many solutions for x and y.

You do not need to find all of them. I only want one of them, preferably expressed in terms of M and N.

Thanks.