The Indecomposable Solutions of Linear Congruences

2017/03/10 by Klaus Pommerening, Pommerening, Klaus
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1703.03708

Abstract

This article considers the minimal non-zero (= indecomposable) solutions of the linear congruence 1⋅ x₁ + ⋯ + (m-1)⋅ x_m-1 ≡ 0 \pmod m for unknown non-negative integers x₁, …, x_n, and characterizes the solutions that attain the Eggleton-Erdős bound. Furthermore it discusses the asymptotic behaviour of the number of indecomposable solutions. The results have direct interpretations in terms of zero-sum sequences and invariant theory.

Citations

• Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors

Related

• Linear Congruences with Ratios
• An incomplete variant of Wilson's congruence
• On the congruence x^x≡ λ\pmod p
• On the Number of Solutions of Exponential Congruences
• Kloosterman sums with primes and solvability of one congruence with inverse residues. I