freeCodeCamp/curriculum/challenges/portuguese/10-coding-interview-prep/project-euler/problem-157-solving-the-diophantine-equation.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4091000cf542c50ff1c	Problema 157: Resolução da equação diofantina	5	301788	problem-157-solving-the-diophantine-equation

--description--

Considere a equação diofantina \frac{1}{a} + \frac{1}{b} = \frac{p}{{10}^n}, sendo a, b, p, n números inteiros positivos e a ≤ b.

Para n = 1, esta equação tem 20 soluções listadas abaixo:

\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}

Quantas soluções tem esta equação para 1 ≤ n ≤ 9?

--hints--

diophantineEquation() deve retornar 53490.

assert.strictEqual(diophantineEquation(), 53490);

--seed--

--seed-contents--

function diophantineEquation() {

  return true;
}

diophantineEquation();

--solutions--

// solution required