Question

Define r(n, m) : N x Z+ -> N be the remainder obtained when dividing m into n. Define a function fm: N x N -> N as follows: f(n, k) = k if r(n, m) = 0, and f(n, k) = f(n-m, k+ 1) otherwise. Describe in terms of a single well-known arithmetic operation what f(n, 0) is computing.

Answer 1

fm defined on N*N, but 0 is not in N.

Hence f(n,0) is computing nothing, it does not exist.