APMO Power!Number Theory Level 4
If \(a\) and \(b\) are positive integers from \(1\) to \(999\) [inclusive], how many ordered pairs \((a, b)\) are there such that \[(a+36b)(b+36a)\] is an integral power of \(2\)?
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.