CYCLOTOMIC COSETS IN THE RING EQUATION

We consider the ringR_(4p^n q^m )=GF(l)[x]/(x^(4p^n q^m )-1) where p,q,l are distinct odd primes,l is a primitive root both modulo p^n and q^m such that gcd (p^n), (q^m)) d.Explicit expressions for all the 4(m n d m n 1) Cyclotomic Cosets areobtained, p does not divide q 1 .