We describe a method for establishing that values from a fixed polynomial sequence are represented frequently by some prescribed sum of powers of natural numbers. As an illustration of this method, we show that for at least X-129/136 of the integers n with 1 less than or equal to n less than or equal to X, a fixed quadratic polynomial phi(n) may be written as the sum of five cubes of positive integers. A similar result is established for the sum of a square and three cubes of positive integers.
|Number of pages
|Quarterly Journal of Mathematics
|Published - Dec 2001
- WARING PROBLEM