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Tag Archives: polynomials
An arithmetic van der Corput trick and the polynomial van der Waerden theorem
The van der Corput difference theorem (or trick) was develop (unsurprisingly) by van der Corput, and deals with uniform distribution of sequences in the torus. Theorem 1 (van der Corput trick) Let be a sequence in a torus . If … Continue reading
New polynomial and multidimensional extensions of classical partition results
Vitaly Bergelson, John Johnson and I recently uploaded to the arXiv a paper entitled “New polynomial and multidimensional extensions of classical partition results“. In this post I will give some motivating examples for the results in the paper. To keep … Continue reading
Posted in Combinatorics, paper, Ramsey Theory
Tagged Bergelson, Deuber, Johnson, monochromatic configurations, polynomials, Rado
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Primes of the form x^2+2y^2
In this post I will present a quite nice proof of the following fact from elementary number theory: Theorem 1 Let be a prime number. There are such that if and only if is a quadratic residue . Recall that … Continue reading
Posted in Classic results, Number Theory
Tagged Minkowski's theorem, polynomials, primes
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