MathDB

Lcm fractions

Source: 239 2009 S4

July 29, 2020

number theory

Problem Statement

Natural numbers

a

and

b

are given such that the number

P = \frac{[a, b]}{a + 1} + \frac{[a, b]}{b + 1}

Is a prime. Prove that

4P + 5

is the square of a natural number.