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

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


marked as duplicate by Bill Dubuque elementary-number-theory Feb 1 at 5:09

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

  • $\begingroup$ Ohh ok $(6|p)=(2|p)(3|p)$ if $p \neq 2,3$ then it is always $1$. Thanks $\endgroup$ – Gimgim Feb 1 at 4:55

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