# legendre symbols

• November 13th 2009, 11:12 AM
scubasteve123
legendre symbols
Suppose that p = 87k +4 is prime prove
(29/p)=1
• November 13th 2009, 11:48 AM
tonio
Quote:

Originally Posted by scubasteve123
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 $\left(\begin{array}{c}29\\p\end{array}\right)=\lef t(\begin{array}{c}p\\29\end{array}\right)=\left(\b egin{array}{c}4\\29\end{array}\right)=1$

Tonio