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formal statement (Lean)
409theorem liouville_eq_mobius_of_squarefree {n : ℕ} (hn : n ≠ 0) (hsq : Squarefree n) :
410 liouville n = mobius n := by
proof body
Term-mode proof.
411 rw [liouville_eq hn, mobius_apply_of_squarefree hsq, bigOmega_eq_omega_of_squarefree hn hsq]
412
413/-- μ(n)² = 1 iff n is squarefree. -/
depends on (9)
Lean names referenced from this declaration's body.
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
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bigOmega_eq_omega_of_squarefree
in IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
decl_use
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liouville
in IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
decl_use
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liouville_eq
in IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
decl_use
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mobius
in IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
decl_use
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mobius_apply_of_squarefree
in IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
decl_use