Corpus ID: 232240428

# Distinct residues of Lucas polynomials over \$\mathbb{F}_p\$

```@inproceedings{Brazelton2021DistinctRO,
title={Distinct residues of Lucas polynomials over \\$\mathbb\{F\}\_p\\$},
author={T. Brazelton and J. Harrington and M. Litman and Tony W. H. Wong},
year={2021}
}```
Given a polynomial with integral coefficients, one can inquire about the possible residues it can take in its image modulo a prime p. The sum over these residues can sometimes be computed independently of the choice of prime p; for example, Gauss showed that the sum over quadratic residues vanishes modulo a prime. In this paper we provide a closed form for the sum over distinct residues in the image of Lucas polynomials of arbitrary degree over all primes, and prove a complete characterization… Expand

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