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Source — Euclid's Elements, encoded as an rrxiv paper — rrxiv

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Source — Euclid's Elements, encoded as an rrxiv paper

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VII.24 Proposition VII.24

If two numbers be prime to any number, their product also will be prime to the same.

Proof

If

g cd (a, c) = 1

and

g cd (b, c) = 1

, then any prime dividing

ab

and

c

must divide

a

or

b

(using the descent from VII.23) and would contradict one of the hypotheses.

lines 74–74 in main.tex