MathDB

2

Part of 2014 IMAR Test

Problems(1)

Six consecutive squarish numbers!

Source: IMAR Test 2014 Problem 2

5/14/2015
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.
composite numbersnumber theoryPell equations