Nice divisibility in an odd ring
Source: RMO 2008 - District Round - 12th grade - Problem 3
March 5, 2008
group theoryabstract algebrasuperior algebrasuperior algebra unsolved
Problem Statement
Let be a commutative unitary ring with an odd number of elements.
Prove that the number of solutions of the equation x^2 \equal{} x (in ) divides the number of invertible elements of .