Prove that any two consecutive integers are relativley prime.

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Question from Michael, a student:

Im not very good at proofs and I was wandering if you would be able to help me with the following question:
Prove that any two consecutive integers are relativley prime.
Thanks a million.

Michael,

If they're relatively prime that means they have no common divisor other than 1. Look at some examples of two consecutive integers such as 20 & 21; if something, say d, divided 20 and 21 what would that mean about d dividing 21 - 20?

Penny

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