MathDB

x^x \equiv 1 (mod p)

Source: Miklós Schweitzer 2010 , P1

September 9, 2020

number theory

Problem Statement

Let

p

be prime. Denote by

N (p)

the number of integers

x

for which

1 \leq x \leq p

and x ^ {x} \equiv 1 (\bmod p) Prove that there exist numbers

c <1/2

and

p_ {0}> 0

such that

N (p) \leq p ^ {c}

p \ge p_ {0}