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标题:[求助]Elementary number theory --- gcd
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HJin
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[求助]Elementary number theory --- gcd
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


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2007-06-21 08:42
HJin
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gcd = greatest common divisor

For example,

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

I am working on a system which has no Chinese input. Please don\'t blame me for typing English.
2007-06-21 10:52
HJin
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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.


I am working on a system which has no Chinese input. Please don\'t blame me for typing English.
2007-06-21 14:40
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