On the distribution of torsion points modulo primes

Let $\Bbb A$ be a commutative algebraic group defined over a number field K. For a prime ain K where $\Bbb A$ has good reduction, let N a,n be the number of n-torsion points of the reduction of $\Bbb A$ modulo awhere n is a positive integer. When $\Bbb A$ is of dimension one and n is relatively prime to a fixed finite set of primes depending on $\BbbA{/K}$, we determine the average values of N a,n as the prime avaries. This average value as a function of n always agrees with a divisor function.