Consecutive integers and relatively prime numbers

e2m2a · Sep 5, 2020

Summary:: Interested in the history of the proof.

Consecutive integer numbers are always relatively prime to each other. Does anyone know when this was proved? Was this known since Euclid's time or was this proved in modern times?

fresh_42 · Sep 5, 2020

I assume this has been known since someone observed divisors. It is so elementary that it doesn't even deserve the label 'proof': ##d|a \wedge d|(a+1) \Longrightarrow d|((a+1)-a)=1 \Longrightarrow d\in \{\pm 1\}.##

I don't think there is a book History Of Proofs. The earliest proofs are probably the geometry of the ancient Greeks.

Consecutive integers and relatively prime numbers

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Consecutive integers and relatively prime numbers

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