International Mathematics Competition
for University Students
2018

IMC2018: Day 1, Problem 2

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 \(\displaystyle (-1)^2=1\).

  Solution