What do Frobenius's, Solomon's, and Iwasaki's theorems on divisibility in groups have in common?

Elena K. Brusyanskaya, Anton A. Klyachko, Andrey V. Vasil'ev

Our result contains as special cases the Frobenius theorem (1895) on the number of solutions to the equation $x^n=1$ in a group, the Solomon theorem (1969) on the number of solutio…