A bound for the representability of large numbers by ternary quadratic forms and nonhomogeneous Waring equations

It is proved that equation $n=x^2+y^2+6pz^2$ ($p$ is a large fixed prime) is solvable if natural congruencial conditions are satisfied and $nm^{12}>p^{21}$.
As a consequence the solvability of the equation $n=x^2+y^2+u^3+v^3+z^4+w^{16}+t^{4k+1}$ is proved for all sufficiently large $n$. Bibl. – 13 titles.