20S. Sequences of Consecutive Integers

A37 If is a natural number, prove that the number

is not a perfect square.

A9 Prove that among any ten consecutive positive integers at least one is relatively prime to the product of the others.

O51 Prove the among consecutive integers it is always possible to find one which is relatively prime to all the rest.

Here is the official solution file: PEN A9 A37 O51