Computers as novel mathematical reality: V. Easier Waring problem

In this part I continue the discussion of role computers in current research on additive number theory, particular solution easier Waring problem. This problem consists finding for each natural k smallest such s =v(k) that all numbers n can be written as sums integer k-th powers = ± x1k ... xsk with signs. turned out to much harder than original It is intimately related many other problems arithmetic and diophantine geometry. discuss various aspects problem, several further problems, rational finite fields, rings, polynomials, special emphasys connection polynomial identities their solution. As today, these are quite far from being fully solved, provide extremely broad terrain both use education, amateur computer assisted exploration.