legendre symbols

scubasteve123 · #1 $Old$ November 13th, 2009, 12:12 PM

Suppose that p = 87k +4 is prime prove
(29/p)=1

tonio · #2 $Old$ November 13th, 2009, 12:48 PM

Quote:

Originally Posted by scubasteve123 $View Post$

Suppose that p = 87k +4 is prime prove
(29/p)=1

As is easy to see that $p\equiv 4\!\!\!\pmod {29}$ and $29\equiv 1\!\!\!\pmod 4$ , we get by Gauss that $\left(\begin{array}{c}29\\p\end{array}\right)=\left(\begin{array}{c}p\\29\end{array}\right)=\left(\begin{array}{c}4\\29\end{array}\right)=1$

Tonio