yaworsw/euler-manager

---
:id: 157
:name: Solving the diophantine equation <sup>1</sup>/<sub><var>a</var></sub>+<sup>1</sup>/<sub><var>b</var></sub>=
  <sup><var>p</var></sup>/<sub>10<sup><var>n</var></sup></sub>
:url: https://projecteuler.net/problem=157
:content: "Consider the diophantine equation <sup>1</sup>/<sub><var>a</var></sub>+<sup>1</sup>/<sub><var>b</var></sub>=
  <sup><var>p</var></sup>/<sub>10<sup><var>n</var></sup></sub> with <var>a, b, p,
  n</var> positive integers and <var>a</var> ≤ <var>b</var>.  \nFor <var>n</var>=1
  this equation has 20 solutions that are listed below:\n\n| <sup>1</sup>/<sub>1</sub>+<sup>1</sup>/<sub>1</sub>=<sup>20</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>1</sub>+<sup>1</sup>/<sub>2</sub>=<sup>15</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>1</sub>+<sup>1</sup>/<sub>5</sub>=<sup>12</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>1</sub>+<sup>1</sup>/<sub>10</sub>=<sup>11</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>2</sub>+<sup>1</sup>/<sub>2</sub>=<sup>10</sup>/<sub>10</sub>
  |\n| <sup>1</sup>/<sub>2</sub>+<sup>1</sup>/<sub>5</sub>=<sup>7</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>2</sub>+<sup>1</sup>/<sub>10</sub>=<sup>6</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>3</sub>+<sup>1</sup>/<sub>6</sub>=<sup>5</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>3</sub>+<sup>1</sup>/<sub>15</sub>=<sup>4</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>4</sub>+<sup>1</sup>/<sub>4</sub>=<sup>5</sup>/<sub>10</sub>
  |\n| <sup>1</sup>/<sub>4</sub>+<sup>1</sup>/<sub>20</sub>=<sup>3</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>5</sub>+<sup>1</sup>/<sub>5</sub>=<sup>4</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>5</sub>+<sup>1</sup>/<sub>10</sub>=<sup>3</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>6</sub>+<sup>1</sup>/<sub>30</sub>=<sup>2</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>10</sub>+<sup>1</sup>/<sub>10</sub>=<sup>2</sup>/<sub>10</sub>
  |\n| <sup>1</sup>/<sub>11</sub>+<sup>1</sup>/<sub>110</sub>=<sup>1</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>12</sub>+<sup>1</sup>/<sub>60</sub>=<sup>1</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>14</sub>+<sup>1</sup>/<sub>35</sub>=<sup>1</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>15</sub>+<sup>1</sup>/<sub>30</sub>=<sup>1</sup>/<sub>10</sub>
  | <sup>1</sup>/<sub>20</sub>+<sup>1</sup>/<sub>20</sub>=<sup>1</sup>/<sub>10</sub>
  |\n\nHow many solutions has this equation for 1 ≤ <var>n</var> ≤ 9?\n\n"