Skip to content

fix(Wikipedia/WallSunSun): assume the discriminant is 0 or 1 mod 4 #1528

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
YaelDillies merged 3 commits into from
Jan 9, 2026
Merged

fix(Wikipedia/WallSunSun): assume the discriminant is 0 or 1 mod 4 #1528

Changes from all commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
1e04ea7
fix `infinite_isWallSunSunPrime_of_disc_eq`
mo271 Jan 7, 2026
e3123f0
better fix
YaelDillies Jan 9, 2026
72b1c9a
missing cond
YaelDillies Jan 9, 2026
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
5 changes: 3 additions & 2 deletions FormalConjectures/Wikipedia/WallSunSun.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -48,6 +48,7 @@ The discriminant of this number is the quantity $a^2 - 4b$. It is conjectured th
infinitely many Lucas–Wieferich primes of any given discriminant.
-/
@[category research open, AMS 11]
theorem infinite_isWallSunSunPrime_of_disc_eq (D : ℕ+) :
{p : ℕ | ∃ a b : ℕ, a ^ 2 - 4 * b = D ∧ IsLucasWieferichPrime a b p }.Infinite := by
theorem infinite_isWallSunSunPrime_of_disc_eq {D : ℕ} (hD₀ : 0 < D)
(hD : D ≡ 0 [MOD 4] ∨ D ≡ 1 [MOD 4]) :
{p : ℕ | ∃ a b : ℕ, a ^ 2 - 4 * b = D ∧ IsLucasWieferichPrime a b p}.Infinite := by
Copy link
Member

@eric-wieser eric-wieser Jan 19, 2026

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Should this be integer subtraction instead of nat subtraction?

Copy link
Member

@YaelDillies YaelDillies Jan 20, 2026

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

That doesn't change the mathematical content since D > 0

Copy link
Member

@eric-wieser eric-wieser Jan 20, 2026

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Why do we have D>0 in the first place? I don't see it in the english.

Copy link
Member

@YaelDillies YaelDillies Jan 20, 2026

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

This is a mess. The Wikipedia conjecture is unsourced, and I cannot find back the source in an hour of searching... In the future we should enforce that conjectures are sourced

Copy link
Member

@eric-wieser eric-wieser Jan 20, 2026

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

My guess is that we added the condition ourselves to avoid this being incorrect when the subtraction truncates.

Copy link
Member

@YaelDillies YaelDillies Jan 21, 2026

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

No, this seems wrong. D is supposed to be the discriminant of a quadratic field, so it certainly cannot be a square

Copy link
Member

@YaelDillies YaelDillies Jan 21, 2026

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

#1813

sorry
Loading