radical_thirty
plain-language theorem explainer
The equality rad(30) = 30 holds for the square-free integer 30. Number theorists checking basic properties of the radical function on small primes would cite this verification. The proof is a direct native decision that evaluates the definition without intermediate lemmas.
Claim. $rad(30) = 30$, where $rad(n)$ denotes the product of the distinct prime factors of the natural number $n$.
background
The radical is defined as the product of distinct prime factors of $n$. This module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function. The upstream definition states that the radical of $n$ is the product of its distinct prime factors.
proof idea
The proof is a one-line term that applies native_decide to evaluate radical 30 directly from the primeFactors product definition.
why it matters
This equality supplies a concrete check for the radical on a square-free integer and supports the module's arithmetic function interfaces. It fills a basic verification step in the NumberTheory.Primes.ArithmeticFunctions development.
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