Question

solve the linear congruence 27x≡6(mod 53)

Answer 1

$27x\equiv 6\mod 53$

We find gcd$(27, 53)=1$ , the linear congruence has a unique solution.

We multiply the linear congruence by $2$ :

$54x\equiv 12 \mod 53$

$53x+x\equiv 12\mod53$

$x\equiv 12\mod 53$

Answer: $x\equiv 12\mod 53$.