freeCodeCamp/curriculum/challenges/japanese/10-coding-interview-prep/project-euler/problem-451-modular-inverses.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f5311000cf542c510042	Problem 451: Modular inverses	5	302124	problem-451-modular-inverses

--description--

Consider the number 15.

There are eight positive numbers less than 15 which are coprime to 15: 1, 2, 4, 7, 8, 11, 13, 14.

The modular inverses of these numbers modulo 15 are: 1, 8, 4, 13, 2, 11, 7, 14 because

\begin{align} & 1 \times 1\bmod 15 = 1 \\\\ & 2 \times 8 = 16\bmod 15 = 1 \\\\ & 4 \times 4 = 16\bmod 15 = 1 \\\\ & 7 \times 13 = 91\bmod 15 = 1 \\\\ & 11 \times 11 = 121\bmod 15 = 1 \\\\ & 14 \times 14 = 196\bmod 15 = 1 \end{align}

Let I(n) be the largest positive number m smaller than n - 1 such that the modular inverse of m modulo n equals m itself.

So I(15) = 11.

Also I(100) = 51 and I(7) = 1.

Find \sum I(n) for 3 ≤ n ≤ 2 \times {10}^7

--hints--

modularInverses() should return 153651073760956.

assert.strictEqual(modularInverses(), 153651073760956);

--seed--

--seed-contents--

function modularInverses() {

  return true;
}

modularInverses();

--solutions--

// solution required