Arithmetic progressions

Friday, March 27, 2015 - 3:30pm - 4:00pm
Michael Young (Iowa State University)
A $k$-term arithmetic progression is a sequence of the form $a, a+d, a+2d, ... , a+(k-1)d$, where $a$ and $d$ are nonegative integers. Van der Waerden's Theorem states that given a set of colors there exists an interval $[1,n]$ such that any coloring of the integers, using all the colors, will contain a $k$-term arithmetic progression with each term having the same color. Given a set of colors and $k>0$, actually determining $n$, called a \emph{van der Waerden number} has proven to be a very challenging problem.
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