# Legendre Symbol, $(\frac{a}{p})=(\frac{a+1}{p})=1$ [duplicate]

Show that for every prime p ($p>5$) there exist integers $a$ and $b$ with $1\leq a,b\leq p-1$ such that:

$$\left(\frac{a}{p}\right)=\left(\frac{a+1}{p}\right)=1$$

I tried assuming that there was no integers such that the condition above was true, but I couldn't get to any contradiction.

thank you guys for any hint or adivice you could give me.

## marked as duplicate by lulu, Jyrki LahtonenOct 2 '15 at 3:38

• It seems that $b$ is unused in the main statement... Is there something else that should be said? – abiessu Oct 2 '15 at 1:42