1021 B
1021 B
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f4f21000cf542c510005 | Problem 390: Triangles with non rational sides and integral area | 5 | 302055 | problem-390-triangles-with-non-rational-sides-and-integral-area |
--description--
Consider the triangle with sides \sqrt{5}
, \sqrt{65}
and \sqrt{68}
. It can be shown that this triangle has area 9.
S(n)
is the sum of the areas of all triangles with sides \sqrt{1 + b^2}
, \sqrt{1 + c^2}
and \sqrt{b^2 + c^2}
(for positive integers b
and c
) that have an integral area not exceeding n
.
The example triangle has b = 2
and c = 8
.
S({10}^6) = 18\\,018\\,206
.
Find S({10}^{10})
.
--hints--
nonRationalSidesAndIntegralArea()
should return 2919133642971
.
assert.strictEqual(nonRationalSidesAndIntegralArea(), 2919133642971);
--seed--
--seed-contents--
function nonRationalSidesAndIntegralArea() {
return true;
}
nonRationalSidesAndIntegralArea();
--solutions--
// solution required