On the Number of Solutions of Exponential Congruences

Details On the Number of Solutions of Exponential Congruences On the Number of Solutions of Exponential Congruences

2010-03-09

arxiv.org/abs/1003.1997v1

Mathematics

Number Theory

Scientific paper

For a prime $p$ and an integer $a \in \Z$ we obtain nontrivial upper bounds
on the number of solutions to the congruence $x^x \equiv a \pmod p$, $1 \le x
\le p-1$. We use these estimates to estimate the number of solutions to the
congruence $x^x \equiv y^y \pmod p$, $1 \le x,y \le p-1$, which is of
cryptographic relevance.

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