squarefree_seventyseven
plain-language theorem explainer
77 is square-free because its factorization consists of the distinct primes 7 and 11. Number theorists using arithmetic functions within the Recognition Science setup would cite this instance when evaluating the Möbius function on small composites. The proof is a one-line wrapper that invokes native_decide for direct computational verification.
Claim. The positive integer $77$ is square-free.
background
The module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function μ. Squarefree is the predicate that an integer has no squared prime factor in its factorization. This sits among sibling results such as mobius_ne_zero_iff_squarefree that connect the predicate to non-vanishing of μ.
proof idea
The proof is a one-line wrapper that applies native_decide.
why it matters
This supplies a concrete square-freeness fact for 77 inside the arithmetic-functions module. It supports later Möbius applications in the Recognition Science number-theory layer, though the declaration has no recorded downstream uses. It fills a basic instance needed before Dirichlet inversion or inversion formulas can be applied to specific composites.
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