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curriculum/challenges/italian/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 fn,a,b is defined
+
+by fn,a,b(x)≡ax+b mod n for a,b,x integer and 0
+
+You are given that ∑ R(c) for c=C(100 000,k), and 1 ≤ k ≤99 999 ≡628701600 (mod 1 000 000 007). (C(n,k) is the binomial coefficient).
+
+Find ∑ R(c) for c=C(10 000 000,k), and 1 ≤k≤ 9 999 999. Give your answer modulo 1 000 000 007.
+
+# --hints--
+
+`euler445()` should return 659104042.
+
+```js
+assert.strictEqual(euler445(), 659104042);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function euler445() {
+
+  return true;
+}
+
+euler445();
+```
+
+# --solutions--
+
+```js
+// solution required
+```