## Find the number of x

### Find the number of x

Find the number of solution of the equation $2^x=4^y=8^z$ where $x$, $y$ and $z$ are positive integers, $x$ is less than $10000$ and for every $x$ satisfying the equation, sum of digits of $x$ also belongs to the solution set of $x$

"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

### Re: Find the number of x

Here is the solution:

Every logical solution to a problem has its own beauty.

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**Important**: Please make sure that you have read about the**Rules, Posting Permissions and Forum Language**)### Re: Find the number of x

The answer is incorrect. The correct answer is (as we include all poitive, negative integers and zero) $1665$

"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

### Re: Find the number of x

O O... Probably I haven't understood the question.. Does $12$ belong to the solution set?

Every logical solution to a problem has its own beauty.

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**Important**: Please make sure that you have read about the**Rules, Posting Permissions and Forum Language**)### Re: Find the number of x

Yes, the question should be understood as "if $a$ is a valid value of $x$ then the sum of digits of $a$ also has to be a valid value of $x$"

"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

### Re: Find the number of x

If you post a different topic regarding this, that will be better. This topic is discussing a particular problem and you should post replies regarding this problem only.rakeen wrote:Can u post me some properties of Prime.(especially for BdMO)

"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

### Re: Find the number of x

See here:

http://en.wikipedia.org/wiki/Prime_number

http://mathworld.wolfram.com/topics/Pri ... rties.html

http://www.renyi.hu/~p_erdos/1966-11.pdf

http://projecteuclid.org/DPubS?verb=Dis ... age=record

Hope these might help you.

http://en.wikipedia.org/wiki/Prime_number

http://mathworld.wolfram.com/topics/Pri ... rties.html

http://www.renyi.hu/~p_erdos/1966-11.pdf

http://projecteuclid.org/DPubS?verb=Dis ... age=record

Hope these might help you.

One one thing is neutral in the universe, that is $0$.