pith. sign in
theorem

radical_thirty

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
835 · github
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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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