Quick modular solutions question

**Proof_of_life** · May 2nd 2008, 09:22 AM

How do I solve:

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

Thanks!

**Opalg** · May 2nd 2008, 10:17 AM

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.

**Proof_of_life** · May 2nd 2008, 11:11 AM

Yup, I figured it out. Thanks.

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