Let  be the graded polynomial algebra  with the degree of each generator  being 1, where  denotes the prime field of two elements. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for the polynomial algebra as a module over the mod-2 Steenrod algebra,

In this paper, we explicitly determine all admissible monomials for the case  in degree  with s an arbitrary positive integer. Moreover, we study the hit problem of the degree  in for any integer

Steenrod squares, hit problem, polynomial algebra.