Question 57
Find all the pairs positive integers $(x, y)$ with the following property:
If $\alpha, \beta$ are relatively prime and positive divisors of the number $x^3 + y^3$ then $\alpha + \beta - 1$ is a divisor of $x^3 + y^3$.
If $\alpha, \beta$ are relatively prime and positive divisors of the number $x^3 + y^3$ then $\alpha + \beta - 1$ is a divisor of $x^3 + y^3$.