Y by Adventure10, Mango247
Let
be integer,
An element of the set
is called good if there exists some element
of
such that
is divisible by
Furthermore, an element
is called very good if
is divisible by
Let
denote the number of good elements in
and
denote the number of very good elements in
Prove that
![\[v^2+v \leq g \leq n^2-n.\]](//latex.artofproblemsolving.com/1/7/d/17d1c804e41d6e8962faba3fc488b58b1d357550.png)














![\[v^2+v \leq g \leq n^2-n.\]](http://latex.artofproblemsolving.com/1/7/d/17d1c804e41d6e8962faba3fc488b58b1d357550.png)