Proposition: 7.25: Square of Coprime Number is Coprime
Euclid's Formulation
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.
Modern Formulation
If $A$ and $B$ are coprime, then $A^2$ and $B$ are coprime.
Table of Contents
Proofs: 1
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Proofs: 1 2
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016