radical_threehundredsixty
plain-language theorem explainer
The equality rad(360) = 30 holds, with rad the product of distinct prime factors. Number theorists checking concrete values of arithmetic functions in prime-factor computations would cite this instance. The proof is a one-line native decision that evaluates the radical definition directly.
Claim. $rad(360) = 30$, where $rad(n)$ denotes the product of the distinct prime factors of the natural number $n$.
background
This theorem appears in the ArithmeticFunctions module, which supplies lightweight wrappers around Mathlib arithmetic functions and begins with the Möbius function. The upstream radical definition states: 'The radical of n is the product of its distinct prime factors.' It is implemented as radical (n : ℕ) := n.primeFactors.prod id. The module keeps statements lightweight before layering Dirichlet algebra or inversion formulas.
proof idea
The proof is a one-line term that applies native_decide to reduce the equality by direct evaluation of the radical definition.
why it matters
This supplies a verified concrete value for the radical function inside the primes and arithmetic functions layer. It supports basic interface stabilization in the module, though no downstream theorems currently depend on it. The result sits among other small wrappers that prepare for deeper number-theoretic tools without yet touching Recognition Science landmarks such as the forcing chain or RCL.
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