Monochromatic Sums and Products with Additive or Multiplicative Shifts in Natural Numbers
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912536460263424 |
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| author | Huang, Wen Shao, Song Tao, Tianyi Xiao, Rongzhong Yang, Ningyuan |
| author_facet | Huang, Wen Shao, Song Tao, Tianyi Xiao, Rongzhong Yang, Ningyuan |
| contents | In this paper we prove that for any finite coloring of N there are lambda,rho in N such that infinitely many pairs (x,y),(u,v) in N^2 satisfy the sets {lambda x, lambda y, x y, lambda(x+y)} and {u+rho, v+rho, u v+rho, u+v} being monochromatic. Using related arguments we also give two different proofs of a special case of the Milliken--Taylor theorem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_11661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monochromatic Sums and Products with Additive or Multiplicative Shifts in Natural Numbers Huang, Wen Shao, Song Tao, Tianyi Xiao, Rongzhong Yang, Ningyuan Combinatorics Dynamical Systems Number Theory In this paper we prove that for any finite coloring of N there are lambda,rho in N such that infinitely many pairs (x,y),(u,v) in N^2 satisfy the sets {lambda x, lambda y, x y, lambda(x+y)} and {u+rho, v+rho, u v+rho, u+v} being monochromatic. Using related arguments we also give two different proofs of a special case of the Milliken--Taylor theorem. |
| title | Monochromatic Sums and Products with Additive or Multiplicative Shifts in Natural Numbers |
| topic | Combinatorics Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2408.11661 |