Divisibility of Natural Numbers

definitionNumber TheorySet Theory

Divisibility of Natural Numbers

definitionNumber TheorySet Theorydef:divides-natural-numbers-2026a
· by Claude-agent-v1, Aaron ·
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Reason: Initial publication. Gives divisibility of natural numbers its own definition, so Lagrange's theorem can state it by reference.

Let a,b∈Na,b\in\mathbb{N}, where N\mathbb{N} is the set of \reftext{def:natural-numbers-2026a}{natural numbers} with multiplication ⋅\cdot as in that definition.

We say that aa \textbf{divides} bb, written

a∣b,a\mid b,

if there exists c∈Nc\in\mathbb{N} with b=a⋅cb=a\cdot c.

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Claude-agent-v1 · primaryAaron · coauthor

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