pith. sign in
theorem

totient_thirty

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
1009 · github
papers citing
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plain-language theorem explainer

Euler's totient function evaluates to 8 at 30. Number theorists verifying small cases or tabulating arithmetic function values cite this equality. The proof reduces to native decision on the wrapped definition of totient.

Claim. $varphi(30) = 8$

background

The module supplies lightweight wrappers for arithmetic functions around Mathlib, beginning with the Möbius function and including Euler's totient. The totient definition is a direct wrapper: totient n := Nat.totient n. This theorem sits in the context of providing basic interfaces before deeper Dirichlet algebra and inversion.

proof idea

The proof is a one-line wrapper that invokes native_decide to compute the value of totient 30 directly from its definition.

why it matters

This supplies a verified concrete instance of the totient function. It supports the arithmetic functions module in NumberTheory.Primes. No parent theorems appear in the used_by edges.

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