"Nice" representations
Source: Central American Olympiad 2000, problem 6
August 9, 2007
inductionstrong induction
Problem Statement
Let's say we have a nice representation of the positive integer if we write it as a sum of powers of 2 in such a way that there are at most two equal powers in the sum (representations differing only in the order of their summands are considered to be the same).
a) Write down the 5 nice representations of 10.
b) Find all positive integers with an even number of nice representations.