Power-free palindromes and reversed primes

Abstract: Several long-standing conjectures in number theory are related to the digital properties of integers. Historically, such problems have been confined to the realm of elementary number theory, but recently huge breakthroughs have been made by applying deep analytical techniques. In this talk, we discuss some very recent results on this topic, focusing on palindromes and reversed primes. We first establish that for all bases $b \geq 26000$, there exist infinitely many prime numbers $p$ for which $\{ \overleftarrow{p} \}$ is square-free. Furthermore, we demonstrate the existence of infinitely many palindromes (with $n= \overleftarrow{n}$) that are cube-free. This is based on joint work with Daniel R. Johnston.

Mathematics

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2025)