Let's prove that if \(k\) is an integer, then \(\gcd(k, k+1) = 1\). That is, any two consecutive integers are coprime.

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Twitter proof:

— Mathspp (@mathsppblog) November 14, 2020

Let k be an integer and let d be the greatest common divisor of k and k+1. We have that (k+1)/d=k/d+1/d and both (k+1)/d and k/d are integers, so 1/d must be an integer and we can only have d=1.https://t.co/pItsAnueib

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