A SCHUR-TYPE ADDITION THEOREM FOR PRIMES

@article{Li2008ASA,
  title={A SCHUR-TYPE ADDITION THEOREM FOR PRIMES},
  author={Hongze Li and Hao Pan},
  journal={Journal of Number Theory},
  year={2008},
  volume={132},
  pages={117-126}
}
On improving a Schur-type theorem in shifted primes
We show that if N ≥ exp(exp(exp(k))), then any k-colouring of the primes that are less than N contains a monochromatic solution to p1 − p2 = p3 − 1.
Rado's criterion over squares and higher powers
We establish partition regularity of the generalised Pythagorean equation in five or more variables. Furthermore, we show how Rado's characterisation of a partition regular equation remains valid
Bootstrapping partition regularity of linear systems
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    Proceedings of the Edinburgh Mathematical Society
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References

SHOWING 1-10 OF 10 REFERENCES
The Number of Monochromatic Schur Triples
In this paper, we prove that in every 2-coloring of the set {1,? , N } =R?B, one can find at least N2/22 +O(N) monochromatic solutions of the equation x+y=z. This solves a problem of Graham et al. .
Roth's theorem in the primes
We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood
A 2-Coloring of [1, N] Can Have (1/22)N2+O(N) Monochromatic Schur Triples, But Not less!
TLDR
It is proved that the statement of the title, thereby solving the $100 problem of Ron Graham, is correct.
The primes contain arbitrarily long arithmetic progressions
We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemeredi�s theorem, which asserts that any subset of the integers of
On sets of integers containing k elements in arithmetic progression
In 1926 van der Waerden [13] proved the following startling theorem : If the set of integers is arbitrarily partitioned into two classes then at least one class contains arbitrarily long arithmetic
On Λ(p)-subsets of squares
This paper is a follow up of [B1]. It is shown that the sequence of squares {n2|n=1, 2, ...} contains Λ(p)-subsets of “maximal density”, for any givenp>4. The proof is based on the probabilistic
E-mail address: haopan79@yahoo.com.cn Department of Mathematics People's Republic of China
  • E-mail address: haopan79@yahoo.com.cn Department of Mathematics People's Republic of China
  • 2002
Beweis einer Baudet'schen Vermutung, Nieuw Arch
  • Wisk
  • 1927
Jahresb. Deutsche Math. Verein
  • Jahresb. Deutsche Math. Verein
  • 1916