Game values of arithmetic functions

01/19/2021

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by   Douglas E. Iannucci, et al.

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Arithmetic functions in Number Theory meet the Sprague-Grundy function from Combinatorial Game Theory. We study a variety of 2-player heap games induced by standard arithmetic functions, such as divisors, relatively prime numbers, and their negations. For the ruleset induced by the division algorithm, we prove that the relative Sprague-Grundy values tend to 0 with increasing heap sizes.