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Starting with the equation:

$\frac{1}{a}+\frac{1}{b}=\frac{p}{10^n}$,

I reached the equation:

$10^{n-log(p)} = \frac{ab}{a+b}$.

Now given the positive integer $n$, for what integer values of $p$ would the value of:

$10^{n-log(p)}$,

be rational?

Also, given positive integers $n$ and $p$, how would we find positive integer solutions to $a$ and $b$ that satisfy the second equation, where:

$a ≤ b$,

And is it possible to determine, given $n$ and $p$, how many $a$ and $b$ solutions exist?

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    $10^{n - \log p} = \frac{10^n}{p}$ is always rational.2012-08-18
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    This is Project Euler problem 1572012-08-18
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    And we have been asked not to discuss Project Euler problems. (base-10 logarithms? really??)2012-08-18
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    Yes it is, but no where in my question did I ask for an answer to the problem, I asked specifically for integer solutions when given $n$ and $p$. My actual question is purely mathematical.2012-08-18
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    I don't understand how you can't discuss Project Euler problems when there is an entire tag with 44 questions about PE.2012-08-18
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    Khaled, please have a read of http://tea.mathoverflow.net/discussion/1226/project-euler-questions/ and the various links there.2012-08-18
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    @GerryMyerson: That's about mathoverflow. And isn't it weird not discussing a math problem just because self directed people might not have enough self direction?2012-08-18
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    @GerryMeyerson: and one of the resolving points was that the questions were not research. And the thread even points out that euler has forums of it's own. Talking about study is what this site is about. Even self-directed study.2012-08-18
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    @ex0du5, did you read the part that said, "I asked the administrator "hk" at Project Euler for contact by email...He confirms that PE...do not want their participants asking for help elsewhere."? Did you follow the link to http://meta.math.stackexchange.com/questions/1090/re-project-euler-questions? Did you follow the link to http://forum.projecteuler.net/viewtopic.php?f=5&t=2707? It's most decidedly NOT just about mathoverflow. Oh, and do you suppose you could be bothered to spell my name the same way I spell it?2012-08-18
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    @GerryMyerson: I also read the part where he said a distinction was made between those who worked on the question and those who just repeat it. Also, why do we care what some modmin somewhere says? Should we track every homework back to the teacher and ask?2012-08-18
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    @GerryMyerson: Can you give a consistent philosophy on why this site should exist in the first place if self-directed study can't lead to questions on it? Or, is it just that this one case is somehow different? How? Should we track all questions to their source and ask permission to offer assistance?2012-08-18
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    We care because we are decent human beings. All I can do is point you to the discussions we've had. If they don't convince you, nothing I add is likely to convince you. Anyway, this isn't the place to discuss it. Open a thread on meta, if you want to pursue these questions.2012-08-18
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    @ex0du5 All your questions are answered in the [meta thread discussing Project Euler questions](http://meta.math.stackexchange.com/questions/1090/re-project-euler-questions). As you can see there, the community also had varied feelings about it, however the last answer on that page carries a vote total which addresses the current policy. It also mentions that in general if a professor asks for a homework/exam question to be closed/deleted, it has been math.se's policy to comply with that request. Since PE's admin has essentially done the same thing, this is in line with general policy.2012-08-27
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    @MichaelBoratko And to what extent can this be verified? If I had not included the first equation in my question, would you have known this is a PE problem? Would this not affect the amount of answers I would be receiving?2012-08-27
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    @Khaled Since your second equation is not really that far removed from the first equation, I'm guessing it would be fairly obvious for the members here who have seen the original PE problem to see the connection. In general, if a user can surreptitiously disguise a PE question and it is answered here and never recognized as a PE question then that user will have only cheated themselves.2012-08-27

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