On Waring–Goldbach problem involving fourth powers

Abstract: Let denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper it is proved that any sufficiently large integer N satisfying the congruence condition can be represented as the sum of twelve fourth powers of primes and the fourth power of one . This result constitutes an improvement upon that of Ren and Tsang. [Copyright &y& Elsevier]