A theorem of arithmetic and its proof
β Scribed by Euler L.
- Book ID
- 127398766
- Year
- 1849
- Tongue
- English
- Weight
- 71 KB
- Category
- Library
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A particularly well suited induction hypothesis is employed to give a short and relatively direct formulation of van der Waerden's argument which establishes that for any partition of the natural numbers into two classes, one of the classes contains arbitrarily long arithmetic progressions.
We study almost arithmetical multiprogressions, which are defined as certain unions of arithmetical progressions. We prove an addition theorem stating that arbitrary sumsets of such sets are of the same type again. Almost arithmetical multiprogressions appear as sets of lengths in rings of algebraic