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

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 StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Feb 1 at 5:09

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