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- Thread starter eddybob123
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Mark44

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I was not able to open the file. Why not just put the problem and your work directly into the form?

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Ray Vickson

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I was not able to open the file. Why not just put the problem and your work directly into the form?

The statement was: prove that every positive integer can be represented in the form

[tex] \frac{2^a}{3^b} -\sum_{k=0}^b \frac{2^{c_k}}{3^k}, \\

\text{where } a, b, c_k \text{ are integers },1 = c_0 < c_1 < c_2 < \cdots . [/tex]

It does not say whether or not the a and b are allowed to vary with the integer n to be represented, or whether a and/or b are supposed to be fixed.

RGV

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HallsofIvy

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@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.

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HallsofIvy

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Which

@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.

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However it will get just as complicated as in base ten because of all the powers of 2

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HallsofIvy

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However it will get just as complicated as in base ten because of all the powers of 2

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

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I am just looking for an answer, nothing more.

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