Let m and n be two given integers. Alice thinks of a pair of real numbers x, y and then she tells Bob the values of xm+ym and xn+yn, in this order. Bob's goal is to determine the value of xy using that information. Find all values of m and n for which it is possible for Bob to fulfill his wish, whatever numbers that Alice had chosen.
An old problem came to mid while reading this one, I found it was
Complex Equation Conclusion. In that problem we have a case of m=3, n=2 which resulted in 3 valid answers for x+y. That thought applied to this case suggests that there will be a possibility for multiple answers for x and y even when restricted to integers as long as m and n are both larger than one.
Thoughts
