Source: wikibot/van-der-waerden-s-theorem
= Van der Waerden's theorem
{wiki=Van_der_Waerden's_theorem}
Van der Waerden's theorem is a fundamental result in combinatorial mathematics, specifically in the area of Ramsey theory. The theorem states that for any positive integers \\( r \\) and \\( k \\), there exists a minimum integer \\( N \\) such that if the integers \\( 1 \\) to \\( N \\) are colored with \\( r \\) different colors, there will always be a monochromatic arithmetic progression of length \\( k \\).