totient_eight
plain-language theorem explainer
The theorem establishes that Euler's totient function evaluates to 4 at the integer 8. Number theorists checking small cases or building multiplicative function tables would cite this evaluation. The proof is a one-line wrapper that applies native decision procedures directly to the totient definition.
Claim. $varphi(8) = 4$, where $varphi$ denotes Euler's totient function.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function and extending to Euler's totient. The totient definition is the direct wrapper def totient (n : ℕ) : ℕ := Nat.totient n, which counts the integers up to n that are coprime to n. This concrete evaluation at 8 sits inside the primes and arithmetic functions section as a basic verified instance.
proof idea
The proof is a one-line wrapper that invokes native_decide on the totient definition at 8.
why it matters
This supplies a verified base case for totient values inside the arithmetic functions module. It supports downstream number-theoretic constructions in the Recognition framework that rely on prime factorizations and multiplicative functions. No parent theorems are listed among the used_by edges.
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