Char. of Z as being ident. as a countab. reun. of fin. reun. of fin. cyc. subgr.
Source: Romanian National Olympiad 2003, grade x, p.4
August 27, 2019
complex numbersgroup theoryalgebracyclic group
Problem Statement
a) Prove that the sum of all the elements of a finite union of sets of elements of finite cyclic subgroups of the group of complex numbers, is an integer number.
b) Show that there are finite union of sets of elements of finite cyclic subgroups of the group of complex numbers such that the sum of all its elements is equal to any given integer.
Paltin Ionescu