Products of $p$-Adic Valuation Trees

Dillon Snyder

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arXiv · 2308.11718

Products of $p$-Adic Valuation Trees

Dillon Snyder

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Abstract

The study of prime divisibility plays a crucial role in number theory. The $p$-adic valuation of a number is the highest power of a prime, $p$, that divides that number. Using this valuation, we construct $p$-adic valuation trees to visually represent the valuations of a sequence. We investigate how nodes split on trees generated by linear functions with rational coefficients, as well as those formed from a product of linear or lower degree polynomials. We describe the infinite branches of these polynomial trees and the valuations of their terminating nodes.

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Dillon Snyder. 2023-08-22. Products of $p$-Adic Valuation Trees. https://arxiv.org/abs/2308.11718

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