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Dismal Arithmetic

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arxiv 1107.1130 v2 pith:T3VP5Y3F submitted 2011-07-06 math.NT math.CO

David Applegate , Marc LeBrun , N. J. A. Sloane This is my paper · ORCID
classification math.NTmath.CO
keywords arithmeticdigitsdismaldivisorsjustnumbertakewhen
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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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  1. Bioperational Multisets in Various Semi-rings

    math.RA 2019-08 conditional novelty 6.0 of 10

    Every non-unit element of N, Z, Z[i], Z[ω], and Z[√2] is shown to be the sum-product of some non-trivial minimal multiset, with the lunar-arithmetic section containing a false lemma and false example.

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