Consecutive numbers in multiplication tables
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ID: 320653
2026
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Abstract
ABSTRACT A multiplication table of size $x$ is the set of all possible products $a \cdot b$ with $1 \le a, b \le \sqrt{x}$. In this article, we study the number of pairs of consecutive integers in a multiplication table and obtain non-trivial lower and upper bounds of its size. For multiplication rectangle with side lengths $x^{0.088}$ and $x^{0.912}$, we obtain an almost optimal asymptotic, showing evidence of independence of integers lying in multiplication tables.
| Reference Key |
openalex_W7168043319
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|---|---|
| Authors | Tsz Ho Chan |
| Journal | The Quarterly Journal of Mathematics |
| Year | 2026 |
| DOI |
10.1093/qmath/haag023
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| URL | |
| Keywords | Keywords not found |
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