Numbers un,k (1≤k≤n) are defined as follows
u_{1,1}=1, u_{n,k}=\binom{n}{k} - \sum_{d \mid n, d \mid k, d>1} u_{n/d, k/d}.
(the empty sum is defined to be equal to zero). Prove that n∣un,k for every natural number n and for every k (1≤k≤n). symmetrynumber theory proposednumber theory