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Exactly two balanced numbers among n, n+1, n+2 and n+3

Source: Baltic Way 2011

November 6, 2011
Diophantine equationnumber theory proposednumber theory

Problem Statement

An integer n≥1n\ge 1 is called balanced if it has an even number of distinct prime divisors. Prove that there exist infinitely many positive integers nn such that there are exactly two balanced numbers among n,n+1,n+2n,n+1,n+2 and n+3n+3.
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