3

Part of 2018 Centroamerican and Caribbean Math Olympiad

Problems(1)

Centroamerican 2018, problem 3

Source: 2018 Centroamerican and Caribbean Math Olympiad

x, y

be real numbers such that

x-y, x^2-y^2, x^3-y^3

are all prime numbers. Prove that

x-y=3

.
EDIT: Problem submitted by Leonel Castillo, Panama.

number theoryCentroamericanprime numbers