Question 938692
{{{2744/N}}} = perfect square
There must be at least one n such that
{{{2744/N}}} = {{{n^2}}} for the first statement to be true
So, {{{2744/N}}} = {{{n^2/1}}}
Using cross products,
{{{N*n^2}}} = 2744 and
N = {{{2744/n^2}}}
Factoring 2744 gives us 2*19*73
For N to be an integer ( required to be a perfect square ) ,
n^2 must divide into 2*19*73 without remainder.
For this to be true, there need to be at least two duplicate
integers in the numerator.
This means that there does not exist an integer N
such that {{{2744/N}}} is a perfect square.