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Algorithm and mathematical proof
N|ab deduces the existence of K, so that AB = NK.

Gcd(a, n)= 1 deduces the existence of u and v, so UA+VN =1;

Multiply both ends of the above formula by b at the same time, and there is

ua b+ vnb = b；

Substituting into the first formula is: UNK+VNB = B；;

That is, n(uK+vb)=b

So n|b

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