I am working on this.
I see two ways to approach it, one method is below using Pythagorean Triples.
You can state that,
Is there anyone who can show that the equation:
n^4 - n^2*m^2+m^4 = s^2, (where m, n and s are positive integers) has no integer solutions with |n| > |m| except (n^2, m^2) = (1, 0)
I will appreciate it if anyone can give at least a reference where the proof can be found.
Just a thought.Originally Posted by sheryl
We have to prove that there does not exist two integers n and m such that
is a perfect square.
So we equalled it to .
We can solve the equation for and show that the discriminant cannot be zero.
Since the expression is a perfect square, has to be zero which is not possible.
We have also the case in which is a pefect square.