Knowledge point — bezu theorem

Time:2021-1-11

On the understanding of bezu theorem

In number theory, peishu’s theorem is a theorem aboutGreatest common divisorPeishu theorem is named after French mathematician Etienne peishu.

The principle of bezu theorem

Peishu theorem (or bezu theorem) is named after French mathematician Etienne peishu,For any [integer] A, B and their greatest common divisor D, the linear Diophantine equation about [unknown] x and Y (called peishu equation): if a, B are integers and GCD (a, b) = D, then for any integer x, y, ax + by must be a multiple of D. in particular, there must be an integer x, y, so that ax + by = D holds.

inference

a. The necessary and sufficient condition of B [coprime] is that there exists [integer] x, y such that ax + by = 1.Knowledge point -- bezu theorem

I understand that if two numbers a and B are coprime, then we can find X and y such that ax + by = any positive integer!Knowledge point -- bezu theorem

The above understanding can solve the intelligence problem

How to load res liter of water in a liter and B liter barrels?

It can be proved by itself

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