pith. sign in
theorem

totient_two_pow_two

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

Euler's totient function evaluates to 2 at input 4. Number theorists verifying small prime-power values in multiplicative function calculations would cite this equality directly. The proof reduces to a single native_decide tactic that evaluates the wrapped definition at the concrete argument.

Claim. Euler's totient function satisfies $φ(4) = 2$.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function and including Euler's totient. The upstream definition states totient n := Nat.totient n. This supplies a concrete evaluation at the smallest prime power beyond 2 inside the arithmetic-functions interface.

proof idea

The proof is a one-line wrapper that invokes the native_decide tactic on the totient definition applied to 4.

why it matters

This supplies a basic numerical fact for totient at 4 within the arithmetic functions module. It supports downstream calculations involving prime powers but has no direct dependents in the current graph. It aligns with the module's goal of stabilizing basic interfaces before layering Dirichlet algebra.

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