Chapter 17 Search for Monochromatic \(\{a,b,a+b,ab\}\)
Project by: Xiaoyuan Chen.
\(\textbf{Summary:}\) This project was about the following two exercises from the book Fundamentals of Ramsey Theory by Aaron Robertson, published by CRC Press,Taylor and Frances Group, Boca Raton, FL, in 2021:
\(\textbf{Exercise 2.15}\) Show, via computer, that every \(2\)–colouring of \([1,252]\) admits a monochromatic set of the form \(\{a,b,a+b,ab\}\) with \(a\not=b\text{.}\)
\(\textbf{Exercise 2.16}\) Consider the same problem as in Exercise 2.15, but allow \(a=b\text{.}\) What is the minimal \(n\in \mathbb{Z}^+\) such that every \(2\)–colouring of \([1,n]\) admits a monochromatic set of the form \(\{a,b,a+b,ab\}\text{?}\)