# congruence question

• May 5th 2010, 10:58 PM
johndoe3344
congruence question
Prove that the congruence
(x^2 - 2)(x^2 - 17)(x^2 - 34) = 0 (mod p)
has a solution for every prime p.

No idea how to do this, can anyone help?
• May 6th 2010, 07:20 AM
chiph588@
Quote:

Originally Posted by johndoe3344
Prove that the congruence
(x^2 - 2)(x^2 - 17)(x^2 - 34) = 0 (mod p)
has a solution for every prime p.

No idea how to do this, can anyone help?

If $\left(\frac2p\right)=1$ or $\left(\frac{17}{p}\right)=1$ then we're done.

Otherwise $\left(\frac{34}{p}\right)=\left(\frac2p\right)\lef t(\frac{17}{p}\right) = (-1)(-1) = 1$