Question 61
(a) Is it true that, for arbitrary integer $n$ greater than $1$ and distinct positive integers $i$ and $j$ not greater than $n$, the set of any $n$ consecutive integers contains distinct numbers $i'$ and $j'$ whose product $i'j'$ is divisible by the product $ij$?
(b) Is it true that, for arbitrary integer $n$ greater than $2$ and distinct positive integers $i, j, k$ not greater than $n$, the set of any $n$ consecutive integers contains distinct numbers $i', j', k'$ whose product $i'j'k'$ is divisible by the product $ijk$?
(b) Is it true that, for arbitrary integer $n$ greater than $2$ and distinct positive integers $i, j, k$ not greater than $n$, the set of any $n$ consecutive integers contains distinct numbers $i', j', k'$ whose product $i'j'k'$ is divisible by the product $ijk$?