Linear Congruence Equation, a counter example

#shorts #mathonshorts

12x ≡ 7 mod 22

This question has no solutions because gcd of (12, 22)=2, 2 does not divide 7.

In general, for linear congruence equation
𝑎𝑥≡𝑏(𝑚𝑜𝑑 𝑚)
Let d=(a, m),
if d|b, there are d solutions;
if d does not divide b, there are no solutions.