Proposition: 7.30: Euclidean Lemma
(Proposition 30 from Book 7 of Euclid's “Elements”)
If two numbers make some (number by) multiplying one another, and some prime number measures the number (so) created from them, then it will also measure one of the original (numbers).
* For let two numbers $A$ and $B$ make $C$ (by) multiplying one another, and let some prime number $D$ measure $C$.
* I say that $D$ measures one of $A$ and $B$.
see generalized Euclidean lemma.
Table of Contents
- Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016