arXiv (All)
open access
Monochromatic Sums and Products with Additive or Multiplicative Shifts in Natural Numbers
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 proof
Conceptio Open Archive
Analyze & explore related research in Conceptio
Connect this record directly into your research workflow or AI agent. Explore citations across open repositories, query full text, and export structured proof bundles.
This document is indexed with metadata only: full text is not available in the archive for this record. Open the official source ↗
Related documents
- Infinite Sum-Product Configurations in Parallel#1048328
- A 4AP-free permutation of the positive integers#1070248
- Sparse $k$-AP Covering Sets and the Arithmetic Kakeya Conjecture#822448
- Sequence b-colorings in graphs#985835
- De Bruijn Polyominoes#793385
Record · ID 1000467
Retrieved via Conceptio: every document is proof-bundled with source, license, and retrieval metadata.
Retrieved via Conceptio: every document is proof-bundled with source, license, and retrieval metadata.
Bring this data into your agent: Connect via MCP or API · 20 free credits to start · no card required
Read the Docs → · View CLI source on GitHub · Conceptio Open Knowledge Archive
Read the Docs → · View CLI source on GitHub · Conceptio Open Knowledge Archive