Prove Prime p^2+2 is Composite mod 3 #5

[phyguy321]

Prove that if p $$\geq$$ 5 is prime, then p$$^{2}$$ +2 is composite
(hint: work mod 3 and use #5 to show p^2 + 2 has a factor of 3.)

 

[tiny-tim]

Prove that if p $$\geq$$ 5 is prime, then p$$^{2}$$ +2 is composite
(hint: work mod 3 and use #5 to show p^2 + 2 has a factor of 3.)

Hi phyguy321!

Show us what you've tried, and where you're stuck, and then we'll know how to help.

(and … erm … what's #5? )

 

[phyguy321]

The problem is i have no idea of where to start. Modular arithmetic makes no sense to me. and #5 was my other post on modular arithmetic

 

[tiny-tim]

The problem is i have no idea of where to start. Modular arithmetic makes no sense to me. and #5 was https://www.physicsforums.com/showthread.php?t=261171"

Your other post was to prove that for any integer n, n² = 0 or 1 (mod 3).

So n² + 2 = … ? (mod 3).