triangle


Related things - Pythagoras in 3D
Pythagoras's equation x²+y²=z² has an infinite number of integer solutions. The problem may be viewed as that of finding a rectangle such that height and width and the diagonal all have integer values.
rectangle
This problem may be extended into three dimensions, namely the "integer brick problem".
3d
Find integer values for a, b and c so that all the diagonals shown are also integers. This means that all these equations must have integer solutions:

a²+b²=d², a²+c²=e², b²+c²=f² and a²+b²+c²=g²

No solution has ever been found and yet no one has been able to prove that no solution exists. The integer brick problem remains unsolved.
Choose values for a, b and c and the values of d, e, f and g will be computed. If they are all integers, you have solved the problem! Good luck.
Enter positive integers:a:b:c: d: e: f: g: