10 Consecutive Integers contain Coprime Integer/Historical Note

Historical Note on 10 Consecutive Integers contain Coprime Integer
Since this result appeared in $1975$, it has reappeared in a number of places, including examinations and quizzes.

In Volume $149$, pages $313$ to $317$,  refines this result, by going on to demonstrate that any block of $n$ consecutive integers for $2 \le n \le 16$ contains at least one integer which is coprime to the others.