pith. sign in
theorem

gcd_eight_threehundredsixty

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
697 · github
papers citing
none yet

plain-language theorem explainer

The equality gcd(8, 360) = 8 holds for natural numbers. Number theorists using arithmetic functions may cite this instance when simplifying expressions that involve multiples of 8. The verification applies a single native decision procedure that evaluates the gcd directly.

Claim. $gcd(8, 360) = 8$

background

The module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function μ. Statements remain basic here so that deeper Dirichlet algebra and inversion can be added once interfaces stabilize. The present declaration supplies a concrete numerical fact about the gcd operation on the specific pair 8 and 360.

proof idea

The proof is a one-line wrapper that applies the native_decide tactic to compute the gcd value from the definitions of natural-number division.

why it matters

The result anchors a basic divisibility fact inside the arithmetic-functions module that prepares for Möbius-related calculations. It supplies a ready numerical instance for any later work on squarefree properties or inversion formulas. No downstream theorems currently depend on it, and the module documentation notes that such lightweight facts support future layering of Dirichlet algebra.

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