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arXiv · 2412.09124

Binary-ternary collisions and the last significant digit of $n!$ in base 12

Jean-Marc Deshouillers·Pascal Jelinek·Lukas Spiegelhofer
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Abstract

The third-named author recently proved [Israel J. of Math. 258 (2023), 475--502] that there are infinitely many \textit{collisions} of the base-2 and base-3 sum-of-digits functions. In other words, the equation \[ s_2(n)=s_3(n) \] admits infinitely many solutions in natural numbers. We refine this result and prove that every integer $a$ in $\{1, 2, \ldots, 11\}$ appears as the last nonzero digit of $n!$ in base $12$ infinitely often.

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Jean-Marc Deshouillers, Pascal Jelinek, Lukas Spiegelhofer. 2024-12-12. Binary-ternary collisions and the last significant digit of $n!$ in base 12. https://arxiv.org/abs/2412.09124

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