Proposition VII.26 — If two numbers be prime to two numbers, both to each, their …

Proof

g cd (ab, c d) = 1

when

g cd (a, c) = g cd (a, d) = g cd (b, c) = g cd (b, d) = 1

: apply VII.24 twice.

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Depends on (1)

VII.24Proposition VII.24If two numbers be prime to any number, their product also will be prime to the same.

Required by (dependents) (1)

VII.27Proposition VII.27If two numbers be prime to one another, and each by multiplying itself make a certain number, the products will be…

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