Introduction to Euclidean Algorithm

\[\begin{array}&(2,3), &(3,4), &(4,5), &(5,6), &(6,7) \end{array}\]

Andy wrote out a few pairs of consecutive positive integers, as shown above, and he notes that for each of these pairs, both integers do not share any positive common factor other than 1.

He then boldly asserts that no pair of consecutive positive integers share any positive common factor other than 1.

Is he correct?

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