International Mathematics Competition for University Students
July 22 – 28 2018, Blagoevgrad, Bulgaria
Problem 2. Does there exist a field such that its multiplicative group is isomorphic to its additive group?
(Proposed by Alexandre Chapovalov, New York University, Abu Dhabi)
Hint: Consider the images of squares, in particular the images of \(\displaystyle -1\) and \(\displaystyle (-1)^2=1\).