An Algorithm to Solve the Equal-Sum-Product Problem

C. D. Evans; M. A. Nyblom

An Algorithm to Solve the Equal-Sum-Product Problem

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arxiv 1311.3874 v1 pith:5K34NJPR submitted 2013-11-15 cs.DM math.CO

M. A. Nyblom , C. D. Evans This is my paper · ORCID

classification cs.DMmath.CO

keywords algorithmproblemequal-sum-productadditionapplicationbinaryclassconnected

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A recursive algorithm is constructed which finds all solutions to a class of Diophantine equations connected to the problem of determining ordered n-tuples of positive integers satisfying the property that their sum is equal to their product. An examination of the use of Binary Search Trees in implementing the algorithm into a working program is given. In addition an application of the algorithm for searching possible extra exceptional values of the equal-sum-product problem is explored after demonstrating a link between these numbers and the Sophie Germain primes.

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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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