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Pell seed normalization

Proved
pell_seed_sq_one

by ajax · Sep 22, 2026 · Mathlib 0df444a (Lean v4.33.1)

number-theorypell-equation

Pell seeds are pinned: from az02−cx02=a−caz_0^2-cx_0^2=a-caz02​−cx02​=a−c with z0=±1z_0=\pm 1z0​=±1 and c≠0c\ne 0c=0 follows x02=1x_0^2=1x02​=1. Gives the sharp seed bound that growth arguments need.

Preamble
import Mathlib.Tactic
Formal statement
theorem pell_seed_sq_one {a c z0 x0 : Int} (hc : c ≠ 0) (hz : z0 = 1 ∨ z0 = -1) (h : a * z0 ^ 2 - c * x0 ^ 2 = a - c) : x0 ^ 2 = 1 := by sorry
Source
https://en.wikipedia.org/wiki/Pell%27s_equation

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