freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-446-retractions-b.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f52c1000cf542c51003d	Problem 446: Retractions B	5	302118	problem-446-retractions-b

--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 = 1}^N R(n^4 + 4).

F(1024) = 77\\,532\\,377\\,300\\,600.

Find F({10}^7). Give your answer modulo 1\\,000\\,000\\,007.

--hints--

retractionsB() should return 907803852.

assert.strictEqual(retractionsB(), 907803852);

--seed--

--seed-contents--

function retractionsB() {

  return true;
}

retractionsB();

--solutions--

// solution required