We show that the popular and general κ-μ shadowed fading model with integer fading parameters μ and m can be represented as a mixture of squared Nakagami-m̑ (or Gamma) distributions. Thus, its PDF and CDF can be expressed in a closed form in terms of a finite number of elementary functions (powers and exponentials). The main implications arising from such connection are then discussed, which can be summarized as follows. First, the performance evaluation of communication systems operating in κ-μ shadowed fading becomes as simple as if a Nakagami-m̑ fading channel was assumed. Second, the κ-μ shadowed distribution can be used to approximate the κ-μ distribution using a closed-form representation in terms of elementary functions, by choosing a sufficiently large value of m. Finally, restricting the parameters μ and m to take integer values has limited the impact in practice when fitting the κ-μ shadowed fading model to field measurements. As an application example, the average channel capacity of communication systems operating under κ-μ shadowed fading is obtained in closed-form.