Dismal Arithmetic
David Applegate, Marc LeBrun, N. J. A. Sloane

TL;DR
This paper explores the properties of dismal arithmetic, a simplified number system where addition and multiplication are defined by taking the maximum and minimum digits respectively, and investigates its number theory analogues.
Contribution
It introduces and analyzes fundamental number theory concepts within the framework of dismal arithmetic, providing new insights into this simplified mathematical system.
Findings
Identification of prime analogues in dismal arithmetic
Formulas for the number of divisors and sum of divisors
Analysis of the partition function in dismal arithmetic
Abstract
Dismal arithmetic is just like the arithmetic you learned in school, only simpler: there are no carries, when you add digits you just take the largest, and when you multiply digits you take the smallest. This paper studies basic number theory in this world, including analogues of the primes, number of divisors, sum of divisors, and the partition function.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Mathematical and Theoretical Analysis
