a) what is the smallest number of integers that must be selected from {1,2....,30} in order to guarantee that the selection contains five numbers X1, X2,.....,X5 such that 3| < (Xi-Xj), 1<= i, j<= 5? (prove the answer)

b) Generalize the statement in (a): given positive integers n,k and t, such that n>=tk, what is the smallest number of integers that must be selected from {1,2,...,n} in order to guarantee that the selection contains t numbers X1, X2, .....,Xt such that k|(Xi-Xj), 1<= i, j<= t? (no proof needed)