45 lines
926 B
Markdown
45 lines
926 B
Markdown
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---
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id: 5900f5071000cf542c510018
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title: 'Problem 410: Circle and tangent line'
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challengeType: 5
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forumTopicId: 302079
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dashedName: problem-410-circle-and-tangent-line
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---
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# --description--
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Let C be the circle with radius r, x2 + y2 = r2. We choose two points P(a, b) and Q(-a, c) so that the line passing through P and Q is tangent to C.
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For example, the quadruplet (r, a, b, c) = (2, 6, 2, -7) satisfies this property.
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Let F(R, X) be the number of the integer quadruplets (r, a, b, c) with this property, and with 0 < r ≤ R and 0 < a ≤ X.
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We can verify that F(1, 5) = 10, F(2, 10) = 52 and F(10, 100) = 3384. Find F(108, 109) + F(109, 108).
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# --hints--
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`euler410()` should return 799999783589946600.
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```js
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assert.strictEqual(euler410(), 799999783589946600);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler410() {
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return true;
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}
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euler410();
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```
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# --solutions--
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```js
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// solution required
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```
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