On some general solutions of the simple Pell equation

2015/01/24 by Vladimir Pletser, Pletser, Vladimir
Mathematics · Physics and Astronomy · #11D09 #11J70 #11Y65 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1501.06051

openalex publication_date 2015/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two theorems are demonstrated giving analytical expressions of the fundamental solutions of the Pell equation X²-DY²=1 found by the method of continued fractions for two squarefree polynomial expressions of radicands of Richaud-Degert type D of the form D=(f(u))²±2^αn, where D, n>0, α≥0,∈ℤ, and f(u)>0,∈ℤ, any polynomial function of u∈ℤ such that f(u)≡0(mod (2^α-1n)) or f(u)≡(2^α-2n)(mod (2^α-1n)).

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