Further characterizations and properties of exactly covering congruences

AbstractIf every nonnegative integer occurs in exactly one of the m integer sequences ain#&62; + bi (n ⩾ 0.1 ⩽ i ⩽ m), then the system ain + bi is called an exactly covering congruence (ECC). Three characterizations of ECC's in terms of exponential functions, Bernoulli polynomials and Evler polynomials are given, from which several properties of ECC's are deduced, including a method of obtaining from an ECC with m moduli ai several ECC's with ⩽ m moduli