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Two Primes and Five Mixed Fibonacci-Lucas Summands
Abstract
Using the circle method, we prove that every sufficiently large positive integer is a sum of two primes, u Fibonacci numbers and 5−u Lucas numbers for each u∈{1,2,3,4}. All recurrence indices are positive, and terms may be repeated.
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BibTeX
@misc{shen2026primes,
title = {{Two Primes and Five Mixed Fibonacci-Lucas Summands}},
author = {Zhao Shen and Chenghe Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12291},
eprint = {2610.12291},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12291},
}
RIS
TY - UNPB
TI - Two Primes and Five Mixed Fibonacci-Lucas Summands
AU - Zhao Shen
AU - Chenghe Xu
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12291
UR - https://arxiv.org/abs/2610.12291
AB - Using the circle method, we prove that every sufficiently large positive integer is a sum of two primes, u Fibonacci numbers and 5−u Lucas numbers for each u∈{1,2,3,4}. All recurrence indices are positive, and terms may be repeated.
ER -