Counter-examples to a Problem of Cohn on Classifying Characters Original Research Article

Let p be a prime and F be a finite field with q=ps elements. It is well-known that for any nontrivial multiplicative character f of F,[formula] H. Cohn asked whether the converse is true. For the case p is odd and s=1, A. Biró gives a partial positive answer to Cohnʹs problem. In this note, we give a negative answer to Cohnʹs problem when q>4 and s>1.