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Find if the number is irrational

Source: 2019 Jozsef Wildt International Math Competition-W. 15

May 18, 2020
number theory

Problem Statement

It is possible to partition the set {100,101,⋯ ,1000}\{100, 101,\cdots , 1000\} into two subsets so that for any two distinct elements xx and yy belonging to the same subset x+y3 \sqrt[3]{x + y} is irrational?
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