Polymorphic Numbers with Exponential Prefix

2025/12/05 by Samer Seraj, Seraj, Samer · 1 voice
Computer Science · Mathematics · #11A07 #11A63 #11D09 #26A06 #Analytic Number Theory Research #Cryptography and Residue Arithmetic #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #math.HO

paper · pdf · doi:10.48550/arxiv.2512.06057

openalex publication_date 2025/12/05 · arxiv published 2025/12/05 · arxiv updated 2025/12/05 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28

Abstract

We observe that the computation 5² = 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.

Discussions

• Samer Seraj: Polymorphic Numbers with Exponential Prefix https://arxiv.org/abs/2512.06057 https://arxiv.org/pdf/2512.06057 https://arxiv.org/html/2512.06057 [bsky, 0 points, 0 comments]

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