MathDB

Let

p

be a prime number. We construct a directed graph of

p

vertices, labeled with integers from

0

p-1

. There is an edge from vertex

x

to vertex

y

if and only if

x^2+1\equiv y \pmod{p}

. Let

f(p)

denotes the length of the longest directed cycle in this graph. Prove that

f(p)

can attain arbitrarily large values.

Problem Statement