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abc conjecture

AbcConjecturePropdef

The abc conjecture: for every ε > 0 there is a constant K such that whenever coprime positive naturals satisfy a + b = c, we have c ≤ K · radical(abc)^(1+ε). It says that a + b = c cannot be built out of high prime powers on all three sides at once.

def AbcConjectureProp : Prop :=
  ∀ ε : ℝ, 0 < ε → ∃ K : ℝ, ∀ a b c : ℕ, 0 < a → 0 < b → Nat.Coprime a b → a + b = c →
    (c : ℝ) ≤ K * (radical (a * b * c) : ℕ) ^ (1 + ε)

import Conjectura.Statements.Mathematics.NumberTheory.AbcConjecture · maintainer — open · raw source

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