Positive integers are written on the blackboard one after another. The next integer an+1 (to be written after a1,a2,...,an) is an arbitrary integer not representable as a sum of several previous integers taken one or more times (i.e. an+1 is not of the form k1∗ai+k2∗a2+...+kn∗an wherek1, k2,.., kn are non-negative integers). Prove that the process of writing cannot be infinite.(A Belov) number theorycombinatorics