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Irrational numbers

Source: Bulgarian IMO TST 2004, Day 3, Problem 3

July 8, 2013

algebra proposedalgebranumber theory

Problem Statement

Prove that among any

2n+1

irrational numbers there are

n+1

numbers such that the sum of any

k

of them is irrational, for all

k \in \{1,2,3,\ldots, n+1 \}

.

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