projecteuler.net

Dissonant Numbers

Published on Sunday, 10th May 2015, 07:00 am; Solved by 345;
Difficulty rating: 40%

Problem 515

Let d(p,n,0) be the multiplicative inverse of n modulo prime p, defined as n × d(p,n,0) = 1 mod p.
Let d(p,n,k) = $\sum_{i=1}^n$d(p,i,k−1) for k ≥ 1.
Let D(a,b,k) = $\sum$(d(p,p-1,k) mod p) for all primes a ≤ p < a + b.

You are given:

  • D(101,1,10) = 45
  • D(103,102,102) = 8334
  • D(106,103,103) = 38162302

Find D(109,105,105).