Question

2^x+2^y=2^z - x, y, z values must be integers and not powers of 10; prove whether this is true or false for x,y,z values >2.

Answer 1

So the thing I'm trying to prove is:
\[\exists( x,y,z) \subset \mathbb{Z}^+: (x,y,z >2),( x,y,z \neq10), (2^x+2^y = 2^z)\]

Answer 2

An example of a specific x,y, and z will do.
Try
a = 3, b = 3, c = 4

Answer 3

confirm x,y,z >2?
confirm x,y,z != 10?
confirm 2^x + 2^y = 2^z?

Answer 4

My answer's no good, eh?

Answer 5

nope

Answer 6

good try my man

Answer 7

What's wrong with it? Are x and y not allowed to be equal?

Answer 8

they can be

Answer 9

Well then you get infinitely many solutions. Any x,y,z such that
x=y
z = x+1

Answer 10

Oh, and x,z != 10.

Answer 11

oh damn, hang on

Answer 12

sorry wrong question lol

Answer 13

i'll retype it

Answer 14

3,3,4 is just one example.
4,4,5 is another.