# For what primes p...

• Mar 28th 2010, 07:24 PM
NikoBellic
For what primes p...
For what primes p (not 2 or 5) do we have

(10/p) = 1?
• Mar 28th 2010, 07:38 PM
chiph588@
Quote:

Originally Posted by NikoBellic
For what primes p (not 2 or 5) do we have

(10/p) = 1?

$\left(\frac{10}{p}\right) = \left(\frac{2}{p}\right) \left(\frac{5}{p}\right)$

So if $\left(\frac{10}{p}\right)=1$, then $\left(\frac{2}{p}\right)=\left(\frac{5}{p}\right)= 1$ or $\left(\frac{2}{p}\right)=\left(\frac{5}{p}\right)=-1$

Now you can use quadratic reciprocity to find $\left(\frac{2}{p}\right)$ and $\left(\frac{5}{p}\right)$.
• Mar 29th 2010, 06:08 AM
pollardrho06
Nice!