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arXiv · 0709.2723

Finding Almost Squares III

Tsz Ho Chan
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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 $[x^c, 2 x^c]$ with $0 < c < 1$.

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Tsz Ho Chan. 2007-09-17. Finding Almost Squares III. https://arxiv.org/abs/0709.2723

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