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id	title	challengeType	forumTopicId	dashedName
5900f4a31000cf542c50ffb6	Problem 311: Biclinic Integral Quadrilaterals	5	301967	problem-311-biclinic-integral-quadrilaterals

--description--

ABCD is a convex, integer sided quadrilateral with 1 ≤ AB < BC < CD < AD.

BD has integer length. O is the midpoint of BD. AO has integer length.

We'll call ABCD a biclinic integral quadrilateral if AO = CO ≤ BO = DO.

For example, the following quadrilateral is a biclinic integral quadrilateral: AB = 19, BC = 29, CD = 37, AD = 43, BD = 48 and AO = CO = 23.

quadrilateral ABCD, with point O, an midpoint of BD

Let B(N) be the number of distinct biclinic integral quadrilaterals ABCD that satisfy {AB}^2 + {BC}^2 + {CD}^2 + {AD}^2 ≤ N. We can verify that B(10\\,000) = 49 and B(1\\,000\\,000) = 38239.

Find B(10\\,000\\,000\\,000).

--hints--

biclinicIntegralQuadrilaterals() should return 2466018557.

assert.strictEqual(biclinicIntegralQuadrilaterals(), 2466018557);

--seed--

--seed-contents--

function biclinicIntegralQuadrilaterals() {

  return true;
}

biclinicIntegralQuadrilaterals();

--solutions--

// solution required

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