Solutions of Congruences by Means of Divergent Series

It is shown in this note that if the solution, in the form of an infinite power series, of the algebraic equation f(x) = 0 with integral co-efficients, is known, we can derive the solutions (if any) of the congruence f(x)= 0 (mod. Kⁿ) when we have solved it for the special case n = 1.