data/problems/218.yml
---
:id: 218
:name: Perfect right-angled triangles
:url: https://projecteuler.net/problem=218
:content: "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. \nMoreover
it is a primitive right angled triangle as gcd(a,b)=1 and gcd(b,c)=1. \nAlso c
is a perfect square.\n\nWe will call a right angled triangle perfect if \n-it is
a primitive right angled triangle \n-its hypotenuse is a perfect square\n\nWe will
call a right angled triangle super-perfect if \n-it is a perfect right angled triangle
and \n-its area is a multiple of the perfect numbers 6 and 28.\n\nHow many perfect
right-angled triangles with c≤10<sup>16</sup> exist that are not super-perfect?\n\n"