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freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-157-solving-the-diophantine-equation.md
gikf bfc21e4c40 fix(curriculum): clean-up Project Euler 141-160 (#42750)
* fix: clean-up Project Euler 141-160

* fix: corrections from review

Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com>

* fix: corrections from review

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>

* fix: use different notation for consistency

* Update curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-144-investigating-multiple-reflections-of-a-laser-beam.md

Co-authored-by: gikf <60067306+gikf@users.noreply.github.com>

Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com>
Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
2021-07-14 13:05:12 +02:00

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id, title, challengeType, forumTopicId, dashedName
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.

assert.strictEqual(diophantineEquation(), 53490);

--seed--

--seed-contents--

function diophantineEquation() {

  return true;
}

diophantineEquation();

--solutions--

// solution required