$4-2\sqrt{3} = {(\sqrt{3}-1)}^2$ $97-56\sqrt{3} = {(7-4\sqrt{3})}^2$ $3$ is indeed an integer

Why is Pan African problem this easy?

This might seem VERY easy but I'm convinced that it might not be that easy under exam conditions. For example, the South African scores in 2004 were: RSA1: 7 1 7 7 7 0 - 29 - Silver RSA2: 5 1 5 6 7 3 - 27 - Silver RSA3: 7 0 1 7 7 1 - 23 - Bronze RSA4: 0 0 7 7 7 1 - 22 - Bronze Keep in mind that the PAMO contestants are in general very young and unexperienced. South Africa does have quite a strong IMO team (sometimes for example, in 2004, not in 2005) but they send 4 promising youngsters (which are not on the IMO team) to PAMO. And this question in particular - yes, it isn't hard, and South Africa scored only 2/28 on it, but if it was REALLY trivial, they would have scored more marks there. So, I guess it isn't!

When I wrote that PAMO i didn't even know about completing the square By the way, day 2 question 2 was in the SAMO of a year or two before, somehow noone noticed... In general the PAMO is much easier than the IMO, but as Arne said, South Africa (which has the strongest team in Africa) only sends its second, more inexperienced team, so the contentants are not that strong. Usually South Africa's PAMO team goes to the IMO the following year.