The $p$-Adic Valuation Trees for Quadratic Polynomials for Odd Primes

We examine the behavior of the sequences of $p$-adic valuations of quadratic polynomials with integer coefficients for an odd prime $p$ through tree representations. Under this representation, a finite tree corresponds to a periodic sequence, and an infinite tree corresponds to an unbounded sequence...

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Hauptverfasser:	Boultinghouse, Will, Hammett, Emily, Hu, Stephen, Kozhushkina, Olena, Snyder, Rachel, Trulen, Justin
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creator	Boultinghouse, Will Hammett, Emily Hu, Stephen Kozhushkina, Olena Snyder, Rachel Trulen, Justin
description	We examine the behavior of the sequences of $p$-adic valuations of quadratic polynomials with integer coefficients for an odd prime $p$ through tree representations. Under this representation, a finite tree corresponds to a periodic sequence, and an infinite tree corresponds to an unbounded sequence. We use the polynomial coefficients to determine whether the $p$-adic valuation trees are finite or infinite, the number of infinite branches, the number of levels, the valuations at terminating nodes, and their relationship to the corresponding sequences.
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title	The $p$-Adic Valuation Trees for Quadratic Polynomials for Odd Primes
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