Square And Cubes Challenging You

Number Theory Level 5

Find the sum of all possible solutions of \(a^2-b^2\) for the following conditions:

  • \(a\) and \(b\) are positive integers less than 1,000,
  • \(a^3-b^3\) is perfect square number,
  • \(a^3-b^3-3ab=1.\)

Example: If possible solutions of \((a,b)\) are \((2,1)\) and \((3,2)\) then the sum of all \((a^2-b^2)=(4-1)+(9-4)=8\).


Problem Loading...

Note Loading...

Set Loading...