Home / Journals / Uniform Distribution Theory (UDT) / UDT. Volume 21. Issue 1 / Binary-ternary collisions and the last significant digit of $n!$ in base 12

Uniform Distribution Theory
CC: Creative Commons BY: credit must be given to the creator. ND: No derivatives or adaptations of the work are permitted.

Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 21. Issue 1


Published on

June, 2026


Pages

1-14


DOI

https://doi.org/10.66833/UDT-2026-0004

Article

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


Authors

Jean-Marc Deshouillers, Pascal Jelinek and Lukas Spiegelhofer


Abstract

The third-named author recently proved [Israel J. of Math. 258 (2023), 475–502] that there are infinitely many 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 ${1,2, ... ,11}$ appears as the last nonzero digit of $𝑛!$ in base 12 infinitely often.


Citation

Deshouillers, J.-M., Jelinek, P. and Spiegelhofer, L. (2026) Binary-ternary collisions and the last significant digit of n! in base 12. Uniform Distribution Theory. 21(1) 1-14. https://doi.org/10.66833/UDT-2026-0004