Legendre Symbol, $(\frac{a}{p})=(\frac{a+1}{p})=1$

Asked Oct 02 '15 at 01:39

Active Oct 02 '15 at 01:42

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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.

edited Oct 02 '15 at 01:42

asked Oct 02 '15 at 01:39

Phillip M.

1

It seems that $b$ is unused in the main statement... Is there something else that should be said? – abiessu Oct 02 '15 at 01:42
Another related question : http://math.stackexchange.com/a/1221135/204937 – Elaqqad Oct 02 '15 at 18:29

0 Answers0