On Waring-Goldbach problem involving fourth powers

Let Pr 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 N≡13(mod240) can be represented as the sum of twelve fourth powers of primes and the fourth power of one P5. This result constitutes an improvement upon that of Ren and Tsang.