chore(i18n,learn): processed translations (#44851)

curriculum/challenges/japanese/10-coding-interview-prep/project-euler/problem-330-eulers-number.md

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+---
+id: 5900f4b71000cf542c50ffc9
+title: 'Problem 330: Euler''s Number'
+challengeType: 5
+forumTopicId: 301988
+dashedName: problem-330-eulers-number
+---
+
+# --description--
+
+An infinite sequence of real numbers $a(n)$ is defined for all integers $n$ as follows:
+
+$$ a(n) = \begin{cases} 1                                                       & n < 0 \\\\ \displaystyle \sum_{i = 1}^{\infty} \frac{a(n - 1)}{i!} & n \ge 0 \end{cases} $$
+
+For example,
+
+$$\begin{align} & a(0) = \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = e − 1 \\\\ & a(1) = \frac{e − 1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \ldots = 2e − 3 \\\\ & a(2) = \frac{2e − 3}{1!} + \frac{e − 1}{2!} + \frac{1}{3!} + \ldots = \frac{7}{2} e − 6 \end{align}$$
+
+with $e = 2.7182818\ldots$ being Euler's constant.
+
+It can be shown that $a(n)$ is of the form $\displaystyle\frac{A(n)e + B(n)}{n!}$ for integers $A(n)$ and $B(n)$.
+
+For example $\displaystyle a(10) = \frac{328161643e − 652694486}{10!}$.
+
+Find $A({10}^9)$ + $B({10}^9)$ and give your answer $\bmod 77\\,777\\,777$.
+
+# --hints--
+
+`eulersNumber()` should return `15955822`.
+
+```js
+assert.strictEqual(eulersNumber(), 15955822);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function eulersNumber() {
+
+  return true;
+}
+
+eulersNumber();
+```
+
+# --solutions--
+
+```js
+// solution required
+```