903 B
903 B
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3d91000cf542c50feeb | Problem 108: Diophantine Reciprocals I | 5 | 301732 | problem-108-diophantine-reciprocals-i |
--description--
In the following equation x, y, and n are positive integers.
\frac{1}{x} + \frac{1}{y} = \frac{1}{n}
For n
= 4 there are exactly three distinct solutions:
\begin{align} & \frac{1}{5} + \frac{1}{20} = \frac{1}{4}\\\\ \\\\ & \frac{1}{6} + \frac{1}{12} = \frac{1}{4}\\\\ \\\\ & \frac{1}{8} + \frac{1}{8} = \frac{1}{4} \end{align}
What is the least value of n
for which the number of distinct solutions exceeds one-thousand?
--hints--
diophantineOne()
should return 180180
.
assert.strictEqual(diophantineOne(), 180180);
--seed--
--seed-contents--
function diophantineOne() {
return true;
}
diophantineOne();
--solutions--
// solution required