A0 = dr(N) "A General Theory for N = pA + qB with p ≡ 1 (mod q)"

This paper develops a complete theory of linear Diophantine systems N = pA + qB for coprime pairs (p,q) satisfying p ≡ 1 (mod q). The central result establishes that the minimal coefficient A₀ equals the generalised digital root dr_q(N), with a closed formula for the representation count R(p,q;N) and arithmetic progressions.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-04-24
DOI
https://doi.org/10.5281/zenodo.19717296
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

A0 = dr(N) "A General Theory for N = pA + qB with p ≡ 1 (mod q)"

Bilal El Issaoui
Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
article

A0 = dr(N) "A General Theory for N = pA + qB with p ≡ 1 (mod q)"

Bilal El Issaoui
article en

Abstract

This paper develops a complete theory of linear Diophantine systems N = pA + qB for coprime pairs (p,q) satisfying p ≡ 1 (mod q). The central result establishes that the minimal coefficient A₀ equals the generalised digital root dr_q(N), with a closed formula for the representation count R(p,q;N) and arithmetic progressions.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 2%
Algebraic Geometry and Number Theory
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