1.7 KiB
1.7 KiB
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4091000cf542c50ff1c | Problem 157: Solving the diophantine equation | 5 | 301788 | problem-157-solving-the-diophantine-equation |
--description--
Consider the diophantine equation \frac{1}{a} + \frac{1}{b} = \frac{p}{{10}^n} with a, b, p, n positive integers and a ≤ b.
For n = 1 this equation has 20 solutions that are listed below:
\begin{array}{lllll}
\frac{1}{1} + \frac{1}{1} = \frac{20}{10} & \frac{1}{1} + \frac{1}{2} = \frac{15}{10}
& \frac{1}{1} + \frac{1}{5} = \frac{12}{10} & \frac{1}{1} + \frac{1}{10} = \frac{11}{10}
& \frac{1}{2} + \frac{1}{2} = \frac{10}{10} \\\\
\frac{1}{2} + \frac{1}{5} = \frac{7}{10} & \frac{1}{2} + \frac{1}{10} = \frac{6}{10}
& \frac{1}{3} + \frac{1}{6} = \frac{5}{10} & \frac{1}{3} + \frac{1}{15} = \frac{4}{10}
& \frac{1}{4} + \frac{1}{4} = \frac{5}{10} \\\\
\frac{1}{4} + \frac{1}{4} = \frac{5}{10} & \frac{1}{5} + \frac{1}{5} = \frac{4}{10}
& \frac{1}{5} + \frac{1}{10} = \frac{3}{10} & \frac{1}{6} + \frac{1}{30} = \frac{2}{10}
& \frac{1}{10} + \frac{1}{10} = \frac{2}{10} \\\\
\frac{1}{11} + \frac{1}{110} = \frac{1}{10} & \frac{1}{12} + \frac{1}{60} = \frac{1}{10}
& \frac{1}{14} + \frac{1}{35} = \frac{1}{10} & \frac{1}{15} + \frac{1}{30} = \frac{1}{10}
& \frac{1}{20} + \frac{1}{20} = \frac{1}{10}
\end{array}$$
How many solutions has this equation for $1 ≤ n ≤ 9$?
# --hints--
`diophantineEquation()` should return `53490`.
```js
assert.strictEqual(diophantineEquation(), 53490);
```
# --seed--
## --seed-contents--
```js
function diophantineEquation() {
return true;
}
diophantineEquation();
```
# --solutions--
```js
// solution required
```