Question 25
(KOR 3) Let $a,b$ be integers that are not perfect squares. Prove that if
$$x^2-ay^2-bz^2+abw^2=0$$
has a nontrivial solution in integers, then so does
$$x^2-ay^2-bz^2=0.$$
$$x^2-ay^2-bz^2+abw^2=0$$
has a nontrivial solution in integers, then so does
$$x^2-ay^2-bz^2=0.$$