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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EXAMPLE<br />
6x ≡ 5 (mod 9)<br />
has no solution because<br />
gcd(6,9)=3 and 3∤5.<br />
----------------------------------<br />
6x ≡ 3 (mod 9)<br />
2x ≡ 1 (mod 3)<br />
since gcd(6,9)|3<br />
2 -1 ∙2x ≡ 2 -1 ∙1 (mod 3)<br />
x ≡ 2 (mod 3)<br />
x ≡ 2, 5, 8 (mod 9)