Number Theory


Second Edition: The Twin Power Conjecture

Authors: Yuly Shipilevsky

We consider a new conjecture regarding powers of integer numbers and more specifically, we are interesting in existence and finding pairs of integers: n ≥ 2 and m ≥ 2, such that nm = mn. We conjecture that n = 2, m = 4 and n = 4, m = 2 are the only integral solutions. Next, we consider the corresponding generalizations for Hypercomplex Integers: Gaussian and Lipschitz Integers.

Comments: 5 Pages.

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Submission history

[v1] 2019-05-16 16:10:59

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