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I'm attempting to solve:

 FindInstance[a/(b + p) + b/(a + p) + p/(a + b) == 4 && a > 0 && b > 0 && p > 0, {a, b, p}, Integers]

but, after evaluating in Mathematica, I get a message: "FindInstance::nsmet: The methods available to FindInstance are insufficient to find the requested instances or prove they do not exist."

Hint: Please, click on the following link:

Elliptic functions

Thank you!

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  • 1
    $\begingroup$ Please change your title to one that is informative and helps others find this problem and the coming solutions. $\endgroup$ – David G. Stork Oct 30 '18 at 21:52
  • $\begingroup$ [wolframalpha.com/input/?i=x/(y%2Bz)+%2B+y/(z%2Bx)+%2B+z/… W|A may help? $\endgroup$ – Hans Oct 30 '18 at 22:05
  • $\begingroup$ @David G. Stork - The title is fine. This is how this particular problem is known. "Equation-solving" also gives a hint about the problem's mathematical nomenclature. @ Hans: A non-negative integer solution to the problem is: apple = 154476802108746166441951315019919837485664325669565431700026634898253202035277999; banana = 36875131794129999827197811565225474825492979968971970996283137471637224634055579; pineapple = 4373612677928697257861252602371390152816537558161613618621437993378423467772036. $\endgroup$ – Gilmar Rodriguez Pierluissi Oct 31 '18 at 18:07
  • $\begingroup$ The title is absolutely terrible. I did a Google search on "apple, banana, pineapple problem" and got a trivial math problem unrelated to this, then dozens of recipes, particularly smoothies. Wikipedia has nothing on that title. I urge you to try such a search, to see just how uninformative and misleading your title is for those who would like to find this problem on this site. $\endgroup$ – David G. Stork Oct 31 '18 at 21:44
  • $\begingroup$ @David G. Stork: How about "A wonderfully sneaky little equation" as posed by the author at the very end of his essay in: quora.com/… $\endgroup$ – Gilmar Rodriguez Pierluissi Oct 31 '18 at 22:03

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