Biweekly problem no. 50 (June 11 - June 25)
Let a1,a2,...,aN be arbitrary integers. Consider the product over all expressions of the form (aj-ai)/(j-i) where 1≤i<j≤N. Show that the value of this product is again an integer.
The solution to this biweekly problem will be posted after Midsommar.
Previous problems and solution sketches
If you enjoyed this problem and have suggestions for future problems, please e-mail Fabian Burghart about it, and I will use it at some point (and give credit to the person suggesting the problem, of course). Ideally, it should be solvable with "general knowledge" among graduate students, and the solution should avoid extensive calculations .
What is this page about?
Loosely inspired by the daily puzzle of the math department at the university of Oxford, and in order to hopefully bring people from different research areas within our department closer together, the biweekly problems are intended as a bit of mathematical fun, something to discuss with colleagues during a fika, something to ponder over during lunch, or perhaps even as an opportunity for procrastination.
Observe that the name is unfortunately a bit misleading: The problem will be updated around the first and 15th of every month, so biweekly is more of a rough estimate.