Question 54
Given positive integers $a$, $c$ and integer $b$, prove that there exists a positive integer $x$ such that
$$
a^x + x \equiv b \pmod{c},
$$
that is, there exists a positive integer $x$ such that $c$ is a divisor of $a^x + x - b$.
$$
a^x + x \equiv b \pmod{c},
$$
that is, there exists a positive integer $x$ such that $c$ is a divisor of $a^x + x - b$.