Polymorphic Numbers with Exponential Prefix
History and Overview
2025-12-09 v1
Abstract
We observe that the computation has the digital property of the result being equal to the exponent concatenated directly to the left of the base. The generalization to a Diophantine equation and inequality in number bases has been articulated previously, but a comprehensive answer was not available in the literature. We classify and largely parametrize the solutions. Tools that play key roles are the Newton-Raphson method, the arithmetic-geometric means inequality, Pell's equation, and Fermat's little theorem.
Cite
@article{arxiv.2512.06057,
title = {Polymorphic Numbers with Exponential Prefix},
author = {Samer Seraj},
journal= {arXiv preprint arXiv:2512.06057},
year = {2025}
}