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Caveat: The following question is mistaken and wrongly posted here.

A question was posted asking for all natural-number solutions $(a,b)$ of the equation $\surd a+\surd b=\surd2009$. It was near the top of my MSE home page of questions, but I couldn't find it a few hours later. The question came from a problem set in the British Mathematical Olympiad (presumably in 2009). It was tagged [contest-math] and I think with another tag—perhaps [elementary-number-theory] or [number-theory]. I searched generally for 2009, sqrt, surd, British, as well as using the specific route provided by the filter menu (taking care to untick any filter requirements other than the tag [contest-math]), with no results.

Apologies to all. The answer is that I found the problem elsewhere. Just my faulty memory attributed it to MSE and made up the details based on plausible presumption. I will leave the question up for a while, because I think that the replies in the comments are useful.

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    $\begingroup$ Why are you using \surd and not \sqrt? $\endgroup$
    – Asaf Karagila Mod
    Sep 22, 2020 at 14:48
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    $\begingroup$ The original problem can be found at bmos.ukmt.org.uk/home/bmo2-2009.pdf -- it's possible the problem was posted on MSE but deleted. $\endgroup$
    – Barry Cipra
    Sep 22, 2020 at 15:55
  • $\begingroup$ @AsafKaragila : It's just a matter of taste; I don't like vincula, especially in text. But please edit if the surd sign bothers you. $\endgroup$
    – John Bentin
    Sep 22, 2020 at 16:05
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    $\begingroup$ I've also looked for questions posted here with "2009", and it turns up some different problems from the British Math Olympiad that year, but not the one you are looking for. If the post author self-deletes a question, it doesn't appear in the list of recent deletions (under Review > Tools), and that's my guess for what happened here. $\endgroup$
    – hardmath
    Sep 22, 2020 at 16:09
  • $\begingroup$ Do you happen to know whether the question was posted recently? $\endgroup$
    – Martin Sleziak
    Sep 22, 2020 at 16:16
  • $\begingroup$ @MartinSleziak : Sorry, I can't be sure of that; but it did appear today (perhaps because it was answered today). $\endgroup$
    – John Bentin
    Sep 22, 2020 at 16:19
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    $\begingroup$ Two ideas: If you happened to open that particular post, maybe you might be able to find it in your browser history. If it is possible that the question was deleted, you might check recently deleted questions in contest-math tag. (Those result are taken from SEDE, you'll need to wait till the next update. See also: Are there some tools to follow deletions on this site?) $\endgroup$
    – Martin Sleziak
    Sep 22, 2020 at 16:32
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    $\begingroup$ Thank you, @MartinSleziak . The last question of any sort to be deleted on MSE was on 20 September, according to the tool recently deleted questions that you kindly provided a link for. I will try again later, when hopefully the list will be updated. $\endgroup$
    – John Bentin
    Sep 22, 2020 at 17:09
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    $\begingroup$ As mentioned in the linked post, the data in SEDE are updated once a week. So if it was deleted just recently, there is a chance that the next week it would be possible to find it through this query. $\endgroup$
    – Martin Sleziak
    Sep 22, 2020 at 17:45

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Even though it turned out the the problem mentioned in the questions was posted on another site, users of Mathematics Stack Exchange still might be interested to see whether this problem (or similar one) was discussed also here. This is a CW-answer trying to collect some related posts - feel free to add more if you find some of them.

Some generalizations:

Relevant searches:

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