Lemma: Generalized Euclidean Lemma

Let \(p\) be a prime number dividing some number $n > 1$ being a product of of some other numbers $n=\prod_{i=1}^\rho n_i.$ Then $p$ divides at least one of the factors $n_i$, i.e. $p\mid n_i.$ Equivalently, if $p$ does not divide any of the factors of $n$, then it also does not divide $n.$

Proofs: 1 Corollaries: 1

Proofs: 1 2
Propositions: 3

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