# APMO Power!

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.

×