$x \equiv b^u\pmod m$ is a solution of given congruent relation

Question

$b,k \in {\Bbb Z};$ $\operatorname{gcd}(b,m) = 1;$ $\operatorname{gcd}(k,φ(m)) = 1; $ $x^k \equiv b\pmod m$

Show that $x \equiv b^u\pmod m$ is a solution of above congruent relation.
$u$ is the diophantine equation $ku - φ(m)v = 1$ with $u,v \in {\Bbb Z}$

Answer 1

Hint $\ $ Raise $\ x^k\equiv b\ $ to the power $\,u,\,$ using $\,ku \equiv 1\pmod{\phi(m)}$.