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Previous research has shown that Artificial Intelligence is capable of distinguishing between authentic paintings by a given artist and human-made forgeries with remarkable accuracy, provided sufficient training. However, with the limited amount of existing known forgeries, augmentation methods for forgery detection are highly desirable. In this work, we examine the potential of incorporating synthetic artworks into training datasets to enhance the performance of forgery detection. Our investigation focuses on paintings by Vincent van Gogh, for which we release the first dataset specialized for forgery detection. To reinforce our results, we conduct the same analyses on the artists Amedeo Modigliani and Raphael. We train a classifier to distinguish original artworks from forgeries. For this, we use human-made forgeries and imitations in the style of well-known artists and augment our training sets with images in a similar style generated by Stable Diffusion and StyleGAN. We find that the additional synthetic forgeries consistently improve the detection of human-made forgeries. In addition, we find that, in line with previous research, the inclusion of synthetic forgeries in the training also enables the detection of AI-generated forgeries, especially if created using a similar generator.