How to prove that one of $2,3,6$ is a square modulo every prime $p$?

Question

I am thinking in terms of quadratic reciprocity but not getting any clue.

score 3 · Accepted Answer · answered Feb 01 '19 at 04:50

3

what is $$ (2|p) (3|p)(6|p) \; ? $$

answered Feb 01 '19 at 04:50

Will Jagy

Ohh ok $(6|p)=(2|p)(3|p)$ if $p \neq 2,3$ then it is always $1$. Thanks – Ri-Li Feb 01 '19 at 04:55

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