Question 51
Let $k\ge2$ be an integer.
1) Let $n\gt k$ be an integer. Do there exist $n$ positive integers such that any $k$ of them are never collectively coprime, but any $k+1$ of them are always collectively coprime?
2) Does there exist an infinite sequence of positive integers satisfying the two conditions above?
1) Let $n\gt k$ be an integer. Do there exist $n$ positive integers such that any $k$ of them are never collectively coprime, but any $k+1$ of them are always collectively coprime?
2) Does there exist an infinite sequence of positive integers satisfying the two conditions above?