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## 20. Sequences of Consecutive Integers

A37 If $n$ is a natural number, prove that the number

$(n + 1)(n + 2)\cdots(n + 10)$

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 $16$ consecutive integers it is always possible to find one which is relatively prime to all the rest.

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