coprime_fortyfive_thirtyseven
plain-language theorem explainer
45 and 37 share no common prime factors. Number theorists using arithmetic functions for Möbius inversion on specific integers may cite this coprimality fact. The verification proceeds by direct computational decision on the gcd.
Claim. $45$ and $37$ are coprime, i.e., their greatest common divisor equals $1$.
background
The module supplies small wrappers around Mathlib's arithmetic function library, beginning with the Möbius function μ. Statements remain lightweight to support later Dirichlet algebra and inversion once basic interfaces stabilize. This declaration records a concrete coprimality instance for the fixed integers 45 and 37 with no dependence on prior lemmas.
proof idea
A one-line term proof applies the native_decide procedure to confirm the gcd computation directly.
why it matters
It supplies a supporting arithmetic fact inside the module on Möbius footholds. The module keeps statements lightweight before deeper inversion results. No downstream applications or open questions are recorded.
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