Legendre Symbols

Ryan Schipfer 12 Mar 2009 22:21

I was just randomly looking up stuff on Legendre Symbols, and found that there are similar methods for evaluating $(\frac{3}{p})$, $(\frac{5}{p})$, $(\frac{7}{p})$ as there were for evaluating $(\frac{-1}{p})$ or $(\frac{2}{p})$.

For $(\frac{3}{p})$:

+1 if $p \equiv 1,11 \mod 12$

-1 if $p \equiv 5,7 \mod 12$

For $(\frac{5}{p})$:

+1 if $p \equiv 1,4 \mod 5$

-1 if $p \equiv 2,3 \mod 5$

For $(\frac{7}{p})$:

+1 if $p \equiv 1,3,9,19,25,27 \mod 28$

-1 if $p \equiv 5,11,13,15,17,23 \mod 28$