Course notes (chap. 1 Number Theory, chap. 2 ... - McGill University
Course notes (chap. 1 Number Theory, chap. 2 ... - McGill University
Course notes (chap. 1 Number Theory, chap. 2 ... - McGill University
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Algorithm 1.2 ( Euclide gcd(a,b) ) <br />
1: g ⟵ a, g′ ⟵ b, x ⟵ 1, y ⟵ 0, x′ ⟵ 0, y′ ⟵ 1,<br />
2:WHILE g′>0 DO <br />
3: k ⟵ g div g′ <br />
4: g′′ ⟵ g-kg′; x′′ ⟵ x-kx′; y′′ ⟵ y-ky′ <br />
5: g ⟵ g′; x ⟵ x′; y ⟵ y′ <br />
6: g′ ⟵ g′′; x′ ⟵ x′′; y′ ⟵ y′′; <br />
7: ENDWHILE <br />
8: RETURN g,x,y <br />
(Maple igcd, igcdex, 1/x mod n, x^(-1) mod n)