The Polynomial t2(4x−n)2 −2xtn Is Always Admitting a Perfect Square
Abstract
In this article, we prove that for every integer \(n \geq 2\), there exist positive integers \(t\) and \(x\) such that the expression \( E = t^2(4x - n)^2 - 2xtn \) is always a perfect square.
Fields of Study & Subjects
Analytic Number Theory Research
Benford’s Law and Fraud Detection
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Preprints.org
- Publication date
- 6 January 2026
- Document type
- Preprint