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id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f3db1000cf542c50feed | Problem 110: Diophantine Reciprocals II | 5 | 301735 | problem-110-diophantine-reciprocals-ii |
--description--
In the following equation x, y, and n are positive integers.
\frac{1}{x} + \frac{1}{y} = \frac{1}{n}
It can be verified that when n
= 1260 there are 113 distinct solutions and this is the least value of n
for which the total number of distinct solutions exceeds one hundred.
What is the least value of n
for which the number of distinct solutions exceeds four million?
Note: This problem is a much more difficult version of Problem 108 and as it is well beyond the limitations of a brute force approach it requires a clever implementation.
--hints--
diophantineTwo()
should return 9350130049860600
.
assert.strictEqual(diophantineTwo(), 9350130049860600);
--seed--
--seed-contents--
function diophantineTwo() {
return true;
}
diophantineTwo();
--solutions--
// solution required