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Six consecutive squarish numbers!

Source: IMAR Test 2014 Problem 2

May 14, 2015
composite numbersnumber theoryPell equations

Problem Statement

Let ϵ\epsilon  be a positive real number. A positive integer will be called ϵ\epsilon-squarish if it is the product of two integers aa and bb such that 1 < a < b < (1 +\epsilon )a. Prove that there are infinitely many occurrences of six consecutive ϵ\epsilon -squarish integers.
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