The Distribution Of Complete Residue Classes Modulo D On A Reduced Residue System Modulo κ

In this paper we deal with the problem of the distribution of complete residueclasses modulo d on a reduced residue system modulo k by character sums and obtaina general result.The main results obtained in this paper are as follows1.we give two different proofs of Apostol.2.we give a proof of Apostol’s result by character sums.3.we give a general conclusion of Apostol’s result.