Which set is S?

Gilgames · #1 Dec 5, 2006, 09:11 AM

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?

asterisk_man · Dec 5, 2006, 12:34 PM

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?



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