Perfect right-angled triangles
Problem 218Published on Saturday, 22nd November 2008, 01:00 am; Solved by 2024; Difficulty rating: 55%
Consider the right angled triangle with sides a=7, b=24 and c=25.
The area of this triangle is 84, which is divisible by the perfect numbers 6 and 28.
Moreover it is a primitive right angled triangle as gcd(a,b)=1 and gcd(b,c)=1.
Also c is a perfect square.
We will call a right angled triangle perfect if
-it is a primitive right angled triangle
-its hypotenuse is a perfect square
We will call a right angled triangle super-perfect if
-it is a perfect right angled triangle and
-its area is a multiple of the perfect numbers 6 and 28.
How many perfect right-angled triangles with c≤1016 exist that are not super-perfect?