Proposition: Divisors of a Product Of Two Factors, Co-Prime to One Factor Divide the Other Factor

If an integer divides a product of two other integers and if it is co-prime to one of the factors of the product, then it divides the other factor. Formally, for \(a\neq 0\)

\[a\mid bc\wedge a\perp b\Rightarrow a\mid c.\]

Proofs: 1 Corollaries: 1

Corollaries: 1
Proofs: 2 3 4 5

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  1. Landau, Edmund: "Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927