Search for Monochromatic $\{a,b,a+b,ab\}$

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Chapter 17 Search for Monochromatic $\{a,b,a+b,ab\}$

Project by: Xiaoyuan Chen.

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$\textbf{Summary:}$ 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:

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$\textbf{Exercise 2.15}$ Show, via computer, that every

$2$ –colouring of

$[1,252]$ admits a monochromatic set of the form

$\{a,b,a+b,ab\}$ with

$a\not=b\text{.}$

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$\textbf{Exercise 2.16}$ 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

$\{a,b,a+b,ab\}\text{?}$

Chapter 17 Search for Monochromatic {a,b,a+b,ab}\{a,b,a+b,ab\}

Project by: Xiaoyuan Chen.

Chapter 17 Search for Monochromatic $\{a,b,a+b,ab\}$