APMO Power!

If aa and bb are positive integers from 11 to 999999 [inclusive], how many ordered pairs (a,b)(a, b) are there such that (a+36b)(b+36a)(a+36b)(b+36a) is an integral power of 22?


This problem is a reworded version of a problem that appeared at the APMO.


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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