Finding Almost Squares III

Abstract

An almost square of type 2 is an integer $n$ that can be factored in two different ways as $n=a_1{b}_1=a_2{b}_2$ with $a_1$, $a_2$, $b_1$, $b_2\approx \sqrt{n}$. In this paper, we shall improve upon previous result on short intervals containing an almost square of type 2. This leads to an inquiry of finding a short interval around $x$ that contains an integer divisible by some integer in $[x^c,2x^c]$ with $0<c<1$.

10 pages