45 lines
989 B
Markdown
45 lines
989 B
Markdown
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---
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id: 5900f5001000cf542c510013
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title: 'Problem 403: Lattice points enclosed by parabola and line'
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challengeType: 5
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forumTopicId: 302071
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dashedName: problem-403-lattice-points-enclosed-by-parabola-and-line
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---
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# --description--
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For integers a and b, we define D(a, b) as the domain enclosed by the parabola y = x2 and the line y = a·x + b:D(a, b) = { (x, y) | x2 ≤ y ≤ a·x + b }.
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L(a, b) is defined as the number of lattice points contained in D(a, b). For example, L(1, 2) = 8 and L(2, -1) = 1.
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We also define S(N) as the sum of L(a, b) for all the pairs (a, b) such that the area of D(a, b) is a rational number and |a|,|b| ≤ N. We can verify that S(5) = 344 and S(100) = 26709528.
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Find S(1012). Give your answer mod 108.
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# --hints--
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`euler403()` should return 18224771.
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```js
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assert.strictEqual(euler403(), 18224771);
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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 euler403() {
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return true;
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}
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euler403();
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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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