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arXiv · 2608.04391

On the Burgess bound and Pythagorean triples involving primitive roots

Hai-Liang Wu·He-Xia Ni
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Abstract

By combining the recent results of Pierce and Xu on the higher-dimensional Burgess bound with the classical one-dimensional Burgess bound, we prove that for any sufficiently large prime $p$, there exists a Pythagorean triple $(a_p,b_p,c_p)$ with $a_p,b_p,c_p\in\mathbb{Z}\cap(0,p)$ such that $a_pb_p/2$ is a primitive root modulo $p$. This confirms a conjecture of Z.-W. Sun for all sufficiently large primes.

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Hai-Liang Wu, He-Xia Ni. 2026-08-05. On the Burgess bound and Pythagorean triples involving primitive roots. https://arxiv.org/abs/2608.04391

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