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.
If m=1 and n=2, then Bob can find xy because ((x^m+y^m)^2-(x^n+y^n))/2=((x+y)^2-(x^2+y^2))/2=((x^2+2xy+y^2)-(x^2+y^2))/2=2xy/2=xy.
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Posted by Math Man
on 2020-12-29 17:01:27 |
A value that works
