MathDB

A quadruple

(p, a, b, c)

of positive integers is called a Leiden quadruple if -

p

is an odd prime number, -

a, b

, and

c

are distinct and -

ab + 1, bc + 1

and

ca + 1

are divisible by

p

. a) Prove that for every Leiden quadruple

(p, a, b, c)

we have

p + 2 \le \frac{a+b+c}{3}

. b) Determine all numbers

p

for which a Leiden quadruple

(p, a, b, c)

exists with

p + 2 = \frac{a+b+c}{3}

Problem Statement