A note on the exceptional set for sums of unlike powers of primes

In this paper, it is proved that with at most \(O(N^{\frac{13}{96}+\varepsilon })\) $O(N^{\frac{13}{96}+\epsilon })$ exceptions, every sufficiently large even integer satisfying \(n\leqslant N\) $n⩽N$ , \(n\not \equiv 2\,(\textrm{mod}\,3)\) $n\not\equiv 2(\text{mod}3)$ can be represented as the sum of two squares of primes, one cube of primes and three biquadrates of primes. This result constitutes a refinement upon that of the author [6].