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arXiv · 2512.06057

Polymorphic Numbers with Exponential Prefix

Samer Seraj
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Abstract

We observe that the computation $5^2 = 25$ 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.

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Samer Seraj. 2025-12-05. Polymorphic Numbers with Exponential Prefix. https://arxiv.org/abs/2512.06057

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