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This question already has an answer here:

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.

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marked as duplicate by lulu, Jyrki Lahtonen Oct 2 '15 at 3:38

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    $\begingroup$ It seems that $b$ is unused in the main statement... Is there something else that should be said? $\endgroup$ – abiessu Oct 2 '15 at 1:42
  • $\begingroup$ Another related question : math.stackexchange.com/a/1221135/204937 $\endgroup$ – Elaqqad Oct 2 '15 at 18:29