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2

Part of 2023 Indonesia Regional

Problems(1)

Perfect Cubes

Source: Indonesia Regional 2023 Essay Number 2

7/16/2023
Let KK be a positive integer such that there exist a triple of positive integers (x,y,z)(x,y,z) such that x3+Ky,y3+Kz,and z3+Kxx^3+Ky , y^3 + Kz, \text{and } z^3 + Kx are all perfect cubes. (a) Prove that K≠2K \ne 2 and K≠4K \ne 4 (b) Find the minimum value of KK that satisfies.
number theoryperfect cubesIndonesiaRMO