Note on integer powers in sumsets Original Research Article

Let k,m,ngreater-or-equal, slanted2 be integers. Let A be a subset of {0,1,…,n} with 0set membership, variantA and the greatest common divisor of all elements of A is 1. Suppose thatimagewhere l=left ceilingk/mright ceiling. We prove that if mgreater-or-equal, slanted3, or m=2 and k even, then there exists a power of m which can be represented as a sum of k elements (not necessarily distinct) of A.