pith. sign in
theorem

divisors_card_eighthundredforty

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

plain-language theorem explainer

840 has exactly 32 positive divisors. Number theorists checking small arithmetic computations or divisor counts would cite this result when validating basic facts in prime-related modules. The proof is a one-line term that invokes native_decide to evaluate the divisor cardinality directly.

Claim. The number of positive divisors of 840 is 32, that is, $d(840) = 32$.

background

The module supplies lightweight wrappers around Mathlib's arithmetic function library, beginning with the Möbius function μ. This theorem records a concrete small-case computation that fits the module's pattern of stabilizing basic interfaces before layering on Dirichlet algebra. No upstream results are invoked.

proof idea

The proof is a one-line term proof that applies native_decide to compute the equality directly from the definition of the divisor set.

why it matters

It supplies a verified divisor count inside the arithmetic functions module that supports the broader construction of Möbius footholds. No downstream theorems or open questions are linked to it.

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