2021/08/30 by Xander Faber, Faber, Xander, Jon Grantham +1 · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #Commutative Algebra and Its Applications #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2108.13441
openalex publication_date 2021/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We determine all pairs of positive integers (a,b) such that a+b and a × b have the same decimal digits in reverse order: (2,2), (9,9), (3,24), (2,47), (2,497), (2,4997), (2,49997), … We use deterministic finite automata to describe our approach, which naturally extends to all other numerical bases. Our automata are a variation on the notion of Young graphs, which were introduced by Sloane to study ``reverse multiples''.