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

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VII.27 Proposition VII.27

If two numbers be prime to one another, and each by multiplying itself make a certain number, the products will be prime to one another; and if the original numbers by multiplying the products make certain numbers, these will be prime to one another.

Proof

Iterate VII.25:

g cd (a, b) = 1

implies

g cd (a^{n}, b^{m}) = 1

for all

n

,

m

.

lines 74–74 in main.tex