pith. sign in
theorem

squarefree_twothousandthreehundredten

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
1381 · github
papers citing
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plain-language theorem explainer

2310 is squarefree. Number theorists working with the Möbius function cite this fact to confirm that μ(2310) equals -1. The proof is a term-mode native decision procedure that directly evaluates the squarefreeness predicate on the concrete integer.

Claim. The positive integer $2310$ is squarefree, meaning it is not divisible by $p^2$ for any prime $p$.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, centered on the Möbius function μ. Squarefreeness is the property that an integer has no repeated prime factors, which determines when μ(n) is nonzero and equals (-1) raised to the number of distinct primes. The local setting is establishing basic concrete instances before layering Dirichlet inversion or deeper algebra.

proof idea

The proof is a one-line term that applies native_decide to the decidable predicate Squarefree 2310.

why it matters

This supplies a verified base case for Möbius evaluations at 2310 inside the NumberTheory arithmetic functions library. It supports downstream inversion formulas that rely on the squarefree property to fix the sign of μ. The declaration fills a concrete foothold in the module without touching open questions in the Recognition chain.

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