lean_workbook_plus_6511

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Given a prime $p$ with $-5$ as a QR, there exists $a,b$ such that $\frac{a^2+5b^2}{p}=1$ or $2$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_6511 (p : ℕ) (hp : p.Prime) (h : (-5 : ZMod p) = 1 ∨ (-5 : ZMod p) = 2) : ∃ a b : ℤ, (a^2 + 5 * b^2) % p = 1 ∨ (a^2 + 5 * b^2) % p = 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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