IMO Shortlist 1989 problem 25
Dodao/la:
arhiva2. travnja 2012. Let
![a, b \in \mathbb{Z}](/media/m/f/8/a/f8a7fbd1a4f56803e232fc0fdd78d331.png)
which are not perfect squares. Prove that if
![x^2 - ay^2 - bz^2 + abw^2 = 0](/media/m/c/9/7/c9788b44a8ff355f500dc07ec2466efb.png)
has a nontrivial solution in integers, then so does
%V0
Let $a, b \in \mathbb{Z}$ which 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 $$x^2 - ay^2 - bz^2 = 0.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1989