Slim exceptional set for sums of two squares, two cubes, and two biquadrates of primes

摘要

We prove that, with at most O(N17/192+epsilon) exceptions, all even positive integers up to N are expressible in the form p(1)(2) + p(2)(2) + p(3)(3) + p(4)(3) + p(5)(4) + p(6)(4); where p(1); p(2); ... ; p(6) are prime numbers. This gives large improvement of a recent result O(N13/16+epsilon) due to M. Zhang and J. J. Li.