Random Diophantine Equation

Find the number of positive integers \(n\) such that there exists an integer \(m \neq \frac{n}{2}\) such that \(\dfrac{n^3-2m^3}{6m}\) is a perfect square.

\(\)
Details and Assumptions:

  • All perfect squares are integers. For example, \(8^2, 4^2,\) etc. are perfect squares, but \(\left( \dfrac{2}{3} \right) ^2\) isn't.
×

Problem Loading...

Note Loading...

Set Loading...