Finding ALL solutions of the modular arithmetic equation $25x \equiv 10 \pmod{40}$ I am unsure how to solve the following problem. I was able to find similar questions, but had trouble understanding them since they did not show full solutions.
The question:
Find ALL solutions (between $1$ & $40$) to the equation $25x \equiv 10 \pmod{40}$.

It suffices to solve the equation $25x\equiv 10\ (\ mod\ 8\ )$ because modulo $5$, the equation holds no matter what $x$ is.
This gives $x\equiv 2\ (\ mod\ 8\ )$.
I think you can easily find out the solutions now.
