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

curriculum/challenges/japanese/10-coding-interview-prep/project-euler/problem-447-retractions-c.md

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+---
+id: 5900f52c1000cf542c51003e
+title: 'Problem 447: Retractions C'
+challengeType: 5
+forumTopicId: 302119
+dashedName: problem-447-retractions-c
+---
+
+# --description--
+
+For every integer $n > 1$, the family of functions $f_{n, a, b}$ is defined by:
+
+$f_{n, a, b}(x) ≡ ax + b\bmod n$ for $a, b, x$ integer and $0 \lt a \lt n$, $0 \le b \lt n$, $0 \le x \lt n$.
+
+We will call $f_{n, a, b}$ a retraction if $f_{n, a, b}(f_{n, a, b}(x)) \equiv f_{n, a, b}(x)\bmod n$ for every $0 \le x \lt n$.
+
+Let $R(n)$ be the number of retractions for $n$.
+
+$F(N) = \displaystyle\sum_{n = 2}^N R(n)$.
+
+$F({10}^7) ≡ 638\\,042\\,271\bmod 1\\,000\\,000\\,007$.
+
+Find $F({10}^{14})$. Give your answer modulo $1\\,000\\,000\\,007$.
+
+# --hints--
+
+`retractionsC()` should return `530553372`.
+
+```js
+assert.strictEqual(retractionsC(), 530553372);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function retractionsC() {
+
+  return true;
+}
+
+retractionsC();
+```
+
+# --solutions--
+
+```js
+// solution required
+```