%0 Journal Article
%T Three consecutive almost squares
%A Jeremy Rouse
%A Yilin Yang
%J Mathematics
%D 2015
%I arXiv
%R 10.1142/S1793042116500603
%X Given a positive integer $n$, we let ${\rm sfp}(n)$ denote the squarefree part of $n$. We determine all positive integers $n$ for which $\max \{ {\rm sfp}(n), {\rm sfp}(n+1), {\rm sfp}(n+2) \} \leq 150$ by relating the problem to finding integral points on elliptic curves. We also prove that there are infinitely many $n$ for which \[ \max \{ {\rm sfp}(n), {\rm sfp}(n+1), {\rm sfp}(n+2) \} < n^{1/3}. \]
%U http://arxiv.org/abs/1502.00605v2