(a) For which positive numbers n does there exist a sequence x1,x2,...,xn, which contains each of the numbers 1,2,...,n exactly once and for which x1+x2+...+xk is divisible by k for each k=1,2,....,n?
(b) Does there exist an infinite sequence x1,x2,x3,..., which contains every positive integer exactly once and such that x1+x2+...+xk is divisible by k for every positive integer k? number theoryInteger sequenceDivisibility