so consider the representation theory of for example z/p over a finite field f_q ...

6 6*8 6*57

q-1 q^2-1 = (q+1)(q-1) q^3-1 = (q^2+q+1)(q-1)

1+q+...+q^[a*b] = (1+q+...+q^a)(1+q^a+...q^[a*b]) ???....

??something about "cyclotomic reciprocity" here?? or something...