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

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Merged
YaelDillies merged 3 commits into from
Jan 9, 2026
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fix(Wikipedia/WallSunSun): assume the discriminant is 0 or 1 mod 4 #1528

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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
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4 changes: 2 additions & 2 deletions FormalConjectures/Wikipedia/WallSunSun.lean
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Expand Up @@ -48,6 +48,6 @@ 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} (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
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@eric-wieser eric-wieser Jan 19, 2026

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Should this be integer subtraction instead of nat subtraction?

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@YaelDillies YaelDillies Jan 20, 2026

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

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@eric-wieser eric-wieser Jan 20, 2026

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

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@YaelDillies YaelDillies Jan 20, 2026

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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

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@eric-wieser eric-wieser Jan 20, 2026

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

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@YaelDillies YaelDillies Jan 21, 2026

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

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@YaelDillies YaelDillies Jan 21, 2026

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#1813

sorry
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