greater than 
,
,
such that 
is a perfect square but none of the integers 
are perfect squares.
satisfying 
and their sum is an even number, consider the quadratic polynomial:![\[
P(x) = x^2 - (m^2 - m + 1)x + (m^2 - n^2 - m)(n^2 + 1).
\]](http://latex.artofproblemsolving.com/d/5/1/d51aaddfddfe06cc91abfdd3476a155770a8a5fd.png)
are positive integers but are not perfect squares.
Y by Adventure10
Alex has a piece of cheese. He chooses a positive number 
and cuts the piece into several pieces one by one. Every time he chooses a piece and cuts it in the same ratio 
His goal is to divide the cheese into two piles of equal masses. Can he do it?
and cuts the piece into several pieces one by one. Every time he chooses a piece and cuts it in the same ratio 
His goal is to divide the cheese into two piles of equal masses. Can he do it?
.
,
and one with mass 
.
.
works well.
works.
