Linear equations mod n

This is a short lecture about solving linear equations mod n. The most important result is that ax=b (mod n) has a solution if and only gcd(a,n) divides b. For example, 2x=5 (mod 8) has no solution since 2=gcd(2,8) does not divide b=5. Also for example, 2x=5 (mod 9) does have a solution since 1=gcd(2,9) divides b=5.