The recent Numberphile video on the famous Problem 6 of the 1988 IMO (mentioned in a recent answer on this site) got me wondering:
Who came up with this problem in the first place, and how did they come up with it?
The Art of Problem Solving website attributes the problem to Stephan Beck of West Germany, but I have not been able to find any corroboration of this attribution, or any other information about how Beck came up with the problem.
It could be that Beck was familiar with the reduction theory of quadratic forms and came up with the problem that way, but Beck does not seem to be listed in the Mathematics Genealogy Project, and I would be mildly surprised that someone without a doctorate in mathematics would be familiar with that topic. If Beck is still alive then one could ask him directly, but I do not know how to contact him.
For completeness, let me also mention that I found the following paragraph on page 127 of the book Problem-Solving Strategies by Arthur Engel, but it does not answer my question.
The next problem was submitted in 1988 by the FRG. Nobody of the six members of the Australian problem committee could solve it. Two of the members were Georges Szekeres and his wife, both famous problem solvers and problem creators. Since it was a number theoretic problem it was sent to the four most renowned Australian number theorists. They were asked to work on it for six hours. None of them could solve it in this time. The problem committee submitted it to the jury of the XXIX IMO marked with a double asterisk, which meant a superhard problem, possibly too hard to pose. After a long discussion, the jury finally had the courage to choose it as the last problem of the competition. Eleven students gave perfect solutions.
