958 B

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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

1*1 mod 15=1

2*8=16 mod 15=1

4*4=16 mod 15=1

7*13=91 mod 15=1

11*11=121 mod 15=1

14*14=196 mod 15=1

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 ∑I(n) for 3≤n≤2·107

--hints--

euler451() should return 153651073760956.

assert.strictEqual(euler451(), 153651073760956);

--seed--

--seed-contents--

function euler451() {

  return true;
}

euler451();

--solutions--

// solution required

958 B Raw Blame History