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

curriculum/challenges/japanese/10-coding-interview-prep/project-euler/problem-445-retractions-a.md

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+---
+id: 5900f52a1000cf542c51003c
+title: 'Problem 445: Retractions A'
+challengeType: 5
+forumTopicId: 302117
+dashedName: problem-445-retractions-a
+---
+
+# --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 $n$.
+
+You are given that
+
+$$\sum_{k = 1}^{99\\,999} R(\displaystyle\binom{100\\,000}{k}) \equiv 628\\,701\\,600\bmod 1\\,000\\,000\\,007$$
+
+Find $$\sum_{k = 1}^{9\\,999\\,999} R(\displaystyle\binom{10\\,000\\,000}{k})$$ Give your answer modulo $1\\,000\\,000\\,007$.
+
+# --hints--
+
+`retractionsA()` should return `659104042`.
+
+```js
+assert.strictEqual(retractionsA(), 659104042);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function retractionsA() {
+
+  return true;
+}
+
+retractionsA();
+```
+
+# --solutions--
+
+```js
+// solution required
+```