Mathematics, Probability, Combinatorics.
that, we need to find the pairs of integers (p, q) with 0 ≤ p ≤ n and 0 ≤ q such that kp+q = x-n. The number of solutions is one plus the quotient of the euclidean division of x-n by k, and the values of p are all the integers between 0 and (x-n)/k. We have calculated the following expression for