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(x + y)(x^2 + 9y) perfect cube of prime

Source: New Zealand NZMOC Camp Selection Problems 2014 p3

September 19, 2021
perfect cubenumber theory

Problem Statement

Find all pairs (x,y)(x, y) of positive integers such that (x+y)(x2+9y)(x + y)(x^2 + 9y) is the cube of a prime number.
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