# Problem 515: Dissonant Numbers

![graphic](img515.gif)

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) = 38162302Find D(109,105,105).