## Find the number of x

For discussing Olympiad Level Number Theory problems
Avik Roy
Posts: 156
Joined: Tue Dec 07, 2010 2:07 am

### 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

Zzzz
Posts: 172
Joined: Tue Dec 07, 2010 6:28 am
Location: 22° 48' 0" N / 89° 33' 0" E

### Re: Find the number of x

Here is the solution:
Every logical solution to a problem has its own beauty.

Avik Roy
Posts: 156
Joined: Tue Dec 07, 2010 2:07 am

### 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

Zzzz
Posts: 172
Joined: Tue Dec 07, 2010 6:28 am
Location: 22° 48' 0" N / 89° 33' 0" E

### 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.

Avik Roy
Posts: 156
Joined: Tue Dec 07, 2010 2:07 am

### 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

rakeen
Posts: 384
Joined: Thu Dec 09, 2010 5:21 pm
Location: Dhaka

### Re: Find the number of x

Can u post me some properties of Prime.(especially for BdMO)
r@k€€/|/

Avik Roy
Posts: 156
Joined: Tue Dec 07, 2010 2:07 am

### Re: Find the number of x

rakeen wrote:Can u post me some properties of Prime.(especially for BdMO)
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.
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

Masum
Posts: 592
Joined: Tue Dec 07, 2010 1:12 pm

### Re: Find the number of x

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

rakeen
Posts: 384
Joined: Thu Dec 09, 2010 5:21 pm
Location: Dhaka

### Re: Find the number of x

hope I'll have to read TnC for the first time. @Av..
r@k€€/|/