radical_two'
plain-language theorem explainer
Radical of a natural number, defined as the product of its distinct prime factors, equals 2 at input 2. Number theorists using arithmetic functions for square-free decompositions or Möbius setups cite this base evaluation. The proof reduces directly via native decision on the prime factorization definition.
Claim. $rad(2) = 2$, where $rad(n)$ is the product of the distinct prime factors of the natural number $n$.
background
The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function as a foothold for later Dirichlet algebra. The radical is defined upstream as the product of distinct prime factors of $n$. This theorem records the concrete value at the prime 2.
proof idea
One-line wrapper that applies native_decide to the equality, using the upstream definition of radical via primeFactors.prod.
why it matters
Supplies a verified base case for the radical function in the arithmetic functions module. No downstream uses appear yet, but the result anchors prime-specific evaluations that feed into square-free and Möbius handling within the Recognition framework.
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