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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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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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 $0$.