New positron emission tomography (PET) tracers could have a substantial impact on early diagnosis of Alzheimer's disease (AD) and mild cognitive impairment (MCI) progression, particularly if they are accompanied by optimised deep learning methods. To realize the full potential of deep learning for PET imaging, large datasets are required for training. However, dataset sizes are restricted due to limited availability. Meanwhile, most of the AD classification studies have been based on structural MRI rather than PET. In this paper, we propose a novel application of conditional Generative Adversarial Networks (cGANs) to the generation of F-18-florbetapir PET images from corresponding MRI images. Furthermore, we show that generated PET images can be used for synthetic data augmentation, and improve the performance of 3D Convolutional Neural Networks (CNN) for predicting progression to AD. Our method is applied to a dataset of 79 PET images, obtained from Alzheimer's Disease Neuroimaging Initiative (ADNI) database. We generate high quality PET images from corresponding MRIs using cGANs, and we evaluate the quality of generated PET images by comparison to real images. We then use the trained cGANs to generate synthetic PET images from additional MRI dataset. Finally we build a 152-layer ResNet to compare the MCI classification performance using both traditional data augmentation method and our proposed synthetic data augmentation method. Mean Structural Similarity (SSIM) index was 0.95 +/- 0.05 for generated PET and real PET. For MCI progression classification, the traditional data augmentation method showed 75% accuracy while the synthetic data augmentation improved this to 82%.