# Thread: Quick modular solutions question

1. ## Quick modular solutions question

How do I solve:

Find all soultions of $x^2 \equiv$ -23 ( mod 240).

Thanks!

2. Originally Posted by Proof_of_life
Find all soultions of $x^2 \equiv$ -23 ( mod 240).
240 is a multiple of 5, and $-23\equiv2\!\!\!\pmod5$. But the equation $x^2\equiv2\!\!\!\pmod5$ has no solutions. So it doesn't look as though $x^2\equiv-23\!\!\!\pmod{240}$ has any solutions either.

3. Yup, I figured it out. Thanks.