  We extend results of Jagy and Kaplansky and the present authors and show that
for all $k\geq 3$ there are infinitely many positive integers $n$, which cannot
be written as $x^2+y^2+z^k=n$ for positive integers $x,y,z$, where for
$k\not\equiv 0 \bmod 4$ a congruence condition is imposed on $z$. These
examples are of interest as there is no congruence obstruction itself for the
representation of these $n$. This way we provide a new family of
counterexamples to the Hasse principle or strong approximation.
