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Part of 2018 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

2018 pos. integers with sum of squares a cube & sum of cubes a square

Source: Rioplatense Olympiad 2018 level 3 p1

12/11/2018
Determine if there are 20182018 different positive integers such that the sum of their squares is a perfect cube and the sum of their cubes is a perfect square.
sum of cubesPerfect Squareperfect cubenumber theorySum of Squares