Given four equations
a,b,c,d,e,f and g are positive integers.
And the problem is to find a triplet (hard) or prove that there are no pairs. (harder)
This problem is calles the perfect cuboid as if a,b and c are the sides of a cuboid, d,e and f are the face diagonnals and g is the space diagonnal. And all of these are integers.
So lets try to solve this?
For a start, I have shown that for integers x, y and z,
This is because for , a, b, c and g must be in the form given above.