Another Reworded APMO Problem!

How many ordered pairs of non-negative integers (a,b)(a,b) subject to a,b<1000a,b <1000 are there such that both a2+4ba^2+4b and b2+4ab^2+4a are perfect squares?


This problem is a reworded version of a problem that appeared in APMO-1999.


This problem is a part of the set "Olympiads and Contests Around the World - 2". You can see rest of the problems here.

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