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

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VII.28 Proposition VII.28

If two numbers be prime to one another, the sum will also be prime to each of them; and if the sum of two numbers be prime to either of them, the original numbers will also be prime to one another.

Proof

Any common divisor of

a + b

and

a

would also divide

b

(by Common Notion 3), contradicting

g cd (a, b) = 1

. Converse runs the same way.

lines 74–74 in main.tex