The problem asks to prove that the Diophantine equation $x^{3}+y^{3} = (x+y)^{2}+(xy)^{2}$ does not have any solutions in natural numbers $x, y$.

I believe that this problem appeared in the section Задачи наших читателей of the Soviet magazine Квант somewhere between the first issue of 1980 and the last one of 1989. Since I don't know much Russian, I haven't been able to locate it by surfing the archives of the magazine that are available online: to add insult to injury, it seems to me that the section in question of the magazine was not a regular one. I would like to provide the exact reference for this problem in a certain document which I am preparing and that's the main reason that has compelled me to ask you this:

**Did anybody here remember seeing this cute problem in Квант once?** If so, would you be so kind as to provide me with a hint that allows one to find out what the actual issue wherein it appeared was?

Please, let me thank you in advance for your attentive consideration of this query of mine.