# What is a upper bound of $\sum_{b=1}^{p-1}\left(\frac{b^2-a^2}{p}\right)\left(\frac{b^2-1}{p}\right)$ for $a\in \mathbb{Z}-{0}$?

by Nilanjan Bag   Last Updated July 12, 2019 07:20 AM

By weil estimate I can only say, one bound is $$\sqrt{p}$$. Can it be strictly less than $$\sqrt{p}$$? I want to see whether one better bound be given or not.

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