In this paper, we study the structure of nite Frobenius groups whose non-rational or non-real irreducible characters are linear.

In this article, we show that every rational map whose multipliers all lie in a given number field is power map, Chebyshev or Lattès map. This strengthens conjecture by Milnor concerning maps with integer multipliers, which was recently proved Ji and Xie.

It seems easy to accept that rationality involves many features that cannot be summarized in terms of some straightforward formula, such as binary consistency.  However, this recognition does not immediately lead to alternative characterizations that might be regarded as satisfactory, even though the inadequacies of the traditional assumptions of rational behavior standard used in economic theo...

Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is n...