On Waring-Goldbach problem for one square and seventeen fifth powers of primes

In this paper, it is established that every sufficiently large positive integer $n$ subject to $n\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}2)$ can be represented as a sum of one square of prime and seventeen fifth powers of primes, which gives an enhancement upon the previous result of Brüdern and Kawada [1].