 #1
 115
 0
Homework Statement
In the link
Homework Equations
In the link
The Attempt at a Solution
First I tried expanding the sum as a power of 2 over a power of 3, but I failed.
Attachments

10.5 KB Views: 93
The statement was: prove that every positive integer can be represented in the formI was not able to open the file. Why not just put the problem and your work directly into the form?
Which is a question of base 3, pretty much by definition!@Ray a and b are allowed to vary, but they have to be integral.
@Mark I do not know how to use the codes
@HallsofIvy I am pretty sure that the answer does not involve different bases. The expression is merely a subtraction of powers of 2 over powers of 3.
No, it won't. Every integer, written is base three, is, by definition, of the form [itex]\sum_{i=0}^N a_i/3^i[/itex] where each [itex]a_i[/itex], because it is a base 3 digit, is either 0, or 1= 2^{0}, or 2= 2^{1}.However it will get just as complicated as in base ten because of all the powers of 2