Find k∈N such thata.) For any n∈N, there does not exist j∈Z which satisfies the conditions 0≤j≤n−k+1 and (nj),(nj+1),…,(nj+k−1) forms an arithmetic progression.b.) There exists n∈N such that there exists j which satisfies 0≤j≤n−k+2, and (nj),(nj+1),…,(nj+k−2) forms an arithmetic progression.Find all n which satisfies part b.)