Small Pythagorean triples modulo prime powers

2022/01/15 by Stephan Baier, Baier, Stephan, Anup Haldar +1
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2201.05871

openalex publication_date 2022/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p>5 be a fixed prime. We obtain an asymptotic formula related to small solutions of quadratic congruences of the form x₁²+x₂²≡ x₃²\bmodpⁿ where max\|x₁|,|x₂|,|x₃|\≤ p^νn with ν>1/2.

Related

• Asymptotic behavior of small solutions of quadratic congruences in three variables modulo prime powers
• Small Solutions of generic ternary quadratic congruences
• Small solutions to inhomogeneous and homogeneous quadratic congruences modulo prime powers
• Small solutions of generic ternary quadratic congruences to general moduli
• Almost prime Pythagorean triples in thin orbits