Consider the set S which is defined as:

1. (1,1) belongs to S
2. if (x,y) belongs to S, then (y,x) belongs to S
3. if (x,y) belongs to S, then (x,x+2y) belongs to S.

What set is S?

Help: focus on the sum of the numbers in each pair.

Any ideas? :confused:

do you need to show a proof? Try to write out some examples and see what you get.
start with (1,1). If (1,1) is in the set what is the (x,x+2y) that is in the set? If (y,x) is in the set then (x+2y,x) must be in the set also.

I'm saying that s is the set of all positive odd integer pairs who's sum is a positive integer power of 2. I can deduce this from looking at a few examples but I'm not currently able to show it mathematically. Any help?