Tomography is the theory behind scans, e.g. MRI-scans. Most common is continuous tomography where an object is reconstructed from numerous projections. In some cases this is not applicable, because the object changes too quickly or is damaged by making hundreds of projections (by X-rays). In such cases discrete tomography may apply where only few projections are made. The present paper shows how number theory helps to provide insight in the application and structure of discrete tomography.