Proposition: 7.25: Square of Co-prime Number is Co-prime
If two numbers are prime to one another then the number created from (squaring) one of them will be prime to the remaining (number).
* Let $A$ and $B$ be two numbers (which are) prime to one another.
* And let $A$ make $C$ (by) multiplying itself.
* I say that $B$ and $C$ are prime to one another.
If $A$ and $B$ are co-prime, then $A^2$ and $B$ are co-prime.
Table of Contents
Proofs: 1 2
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