I need to solve this diophantine equation using a positive integer $x$: $$x^2 + 42x + 21 \equiv 0 \mod 105$$
I think it will be easier if I could use the prime factors of $105$ to get a system of congruences and then use the Chinese Remainder Theorem. Can I do that? If so, why exactly?
If it's possible, then I would get the factors $3$, $5$ and $7$. But I'm getting stuck in this one: $$x^2 + 42x + 21 \equiv 0 \mod 5 $$
Can anyone show me how to do it properly?