# Legendre Symbol

I have a question about Legendre symbol. Let $a$, $b$ be integers. Let $p$ be a prime not dividing $a$. Show that the Legendre symbol verifies: $$\sum_{m=0}^{p-1} \left(\frac{am+b}{p}\right)=0.$$

I know that $\displaystyle\sum_{m=0}^{p-1} \left(\frac{m}{p}\right)=0$, but how do I connect this with the previous formula? Any help is appreciated.

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Show that as $m$ ranges from $0$ to $p-1$, $am$ ranges over all residue classes modulo $p$, and hence $am+b$ ranges over all residue classes modulo $p$. –  Arturo Magidin Mar 10 '11 at 16:38

Show that as $m$ ranges from $0$ to $p−1$, $am$ ranges over all residue classes modulo $p$, and hence $am+b$ ranges over all residue classes modulo $p$.