336. Using Euler's theorem, find such values of $x$ for which $a x-b$ is divisible by $c$, if $(a, c)=1$.
336. Since by condition $a$ and $c$ are coprime numbers, then $a^{\varphi(c)}-1$ is divisible by $c$, then $b a^{\varphi(c)}-b$ is also divisible by $c$, which can be written as: $a b a^{\varphi}(c)-1-b$, therefore, $x=b a^{\varphi}(c)-1$, hence $x=b a^{\varphi}(c)-1+c t$, where $t$ is any integer (see № 197).