Prunescu and Sauras-Altuzarra showed that all C-recursive sequences of natural numbers have an arithmetic div-mod representation that can be derived from their generating function. This representation consists of computing the quotient of two exponential polynomials and taking the remainder of the result modulo a third exponential polynomial, and works for all integers n ≥ 1. Using a different approach, Prunescu proved the existence of two other representations, one of which is the mod-mod representation, consisting of two successive remainder computations. This result has two weaknesses: the representation works only ultimately, and a correction term must be added to the first exponential polynomial. We show that a mod-mod representation without inner correction term holds for all integers n ≥ 1. This follows directly from the div-mod representation by an arithmetic short-cut from outside.