ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
989 B
989 B
id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f5001000cf542c510013 | Problem 403: Lattice points enclosed by parabola and line | 5 | 302071 | problem-403-lattice-points-enclosed-by-parabola-and-line |
--description--
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 }.
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.
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.
Find S(1012). Give your answer mod 108.
--hints--
euler403() should return 18224771.
assert.strictEqual(euler403(), 18224771);
--seed--
--seed-contents--
function euler403() {
return true;
}
euler403();
--solutions--
// solution required