• Corpus ID: 6493705

Roth ’ s Theorem on 3-term Arithmetic Progressions

@inproceedings{Rahman2015RothS,
  title={Roth ’ s Theorem on 3-term Arithmetic Progressions},
  author={Mustazee Rahman},
  year={2015}
}
This article is a discussion about the proof of a classical theorem of Roth’s regarding the existence of three term arithmetic progressions in certain subsets of the integers. Before beginning with this task, however, we will take a brief look at the history and motivation behind Roth’s theorem. The questions and ideas surrounding this subject may have begun with a wonderful theorem due to van der Warden. 
math.mit.edu
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A conjecture of Erdős, supersingular primes and short character sums

If $k$ is a sufficiently large positive integer, we show that the Diophantine equation $$n (n+d) \cdots (n+ (k-1)d) = y^{\ell}$$ has at most finitely many solutions in positive integers $n, d, y$ and…

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