Pell equation

佩尔方程

Number Theory · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

For a positive nonsquare integer dd, the equation x2−dy2=1x^2-dy^2=1 with integer unknowns x,yx,y.

对正的非平方整数 dd，以整数 x,yx,y 为未知量的方程 x2−dy2=1x^2-dy^2=1。

Example

32−2⋅22=13^2-2\cdot2^2=1, so (x,y)=(3,2)(x,y)=(3,2) solves the equation for d=2d=2.

Usage and distinctions

Some authors include the negative equation with right side -1 under the same name; this entry fixes the right side as +1.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. 张神星 — 代数数论讲义 v2.5 (2024-01-09)，合肥工业大学作者讲义Section 1.3.4, printed page 17, equations with right sides ±1; entry restricted to +1 · Checked 2026-10-14

Translation sources

  1. 张神星 — 代数数论讲义 v2.5 (2024-01-09)，合肥工业大学作者讲义§1.3.4 佩尔方程，printed page 17 · Checked 2026-10-14
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