# 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.

## One Citation

### A conjecture of Erdős, supersingular primes and short character sums

- MathematicsAnnals of Mathematics
- 2020

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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### http://math.stanford.edu/~ksound/Notes.pdf Mustazee Rahman University of Toronto, 40 St

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