PreprintCC BY 4.0arXiv
Pythagorean pairs in boxes of prime powers
Abstract
Let pi be the ith prime, and let f(N) be the largest cardinality of a subset of {∏i=1N piai:0≤ ai<N, ai∈ℤ} containing no two distinct legs of an integer right triangle. We prove f(N) ≪ NN (loglog N)−1/1296.
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BibTeX
@misc{xiao2026pythagorean,
title = {{Pythagorean pairs in boxes of prime powers}},
author = {Rongzhong Xiao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11965},
eprint = {2610.11965},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11965},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pythagorean pairs in boxes of prime powers
AU - Rongzhong Xiao
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.11965
UR - https://arxiv.org/abs/2610.11965
AB - Let p_i be the ith prime, and let f(N) be the largest cardinality of a subset of {∏_i=1^N p_i^a_i:0≤ a_i<N, a_i∈ℤ} containing no two distinct legs of an integer right triangle. We prove f(N) ≪ N^N (loglog N)^−1/1296.
ER -