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).
![fig30e](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/euclid/Book07/fig30e.png?raw=true)
Modern Formulation
see generalized Euclidean lemma.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1
Thank you to the contributors under CC BY-SA 4.0!
![](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/calendar-black.png?raw=true)
- Github:
-
![bookofproofs](https://github.com/bookofproofs.png?size=32)
- non-Github:
- @Fitzpatrick
References
Bibliography
- 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