User:Quantum-phantom
This message is regarding [url=https://artofproblemsolving.com/community/c594864h3265596p30137934]this post[/url]. [quote="fura3334"][b]Problem 10[/b] (unclear source) For a positive integer , denote by the number of ways to represent as the sum of powers of 2. Different orders [color=#960000]are[/color] considered different representations, e.g. and are two different representations of . Call "good" if is even. Let be the largest number of consecutive good numbers in . Find the remainder when is divided by 1000.[/quote]
I just read [color=#960000]are[/color] as [color=#960000]aren't[/color]. (yesterday)
Let
We use induction on