MathDB

Simple Italian NT

Source: Italy National Olympiad 2020 P2

September 30, 2020

number theory

Problem Statement

Determine all the pairs

(a,b)

of positive integers, such that all the following three conditions are satisfied: 1-

b>a

and

b-a

is a prime number 2- The last digit of the number

a+b

3

3- The number

ab

is a square of an integer.