Division Criterion for Polynomials F{x}

In this short paper we give a generalization of the two criterion in (4),namely:The first is a necessary and sufficient condition for a polynomial f(x) of coefficients in a field F to be divisible by x^n -1. The second is a necessary and sufficient condition for a polynomial f(x) of coefficients in a field F to be divisible by the cyclotomic polynomial Qp(x) for a prime number p.In addition to these two criterion, we introduce some consequences. An important application of these two criteria is to generate good detecting criteria for error-correcting codes