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A new theoretical method, the generalized transformed characteristic function (GTCF) approach gives an exact, integral solution for the probability density function of the end-to-end received signal-to-noise ratio in multihop amplify-and-forward relaying systems. In turn, the GTCF approach is used to obtain exact integral solutions for the ergodic capacity, outage probability and average symbol error probability of multihop amplify-and-forward relaying systems. The results are precise for any number of hops and can accommodate any channel fading distribution. The theory provides the first exact theoretical solutions for numbers of hops larger than 2.