Davenport's Theorem
Davenport's Theorem is a result in number theory that deals with the sums of subsets of integers. It states that for any finite set of integers, there exists a non-empty subset whose sum is divisible by a given integer. This theorem highlights the existence of certain combinations within a set, emphasizing the relationships between numbers.
The theorem is particularly useful in combinatorial number theory and has applications in various areas, including additive number theory and combinatorial game theory. It provides a foundational understanding of how integers can be combined to achieve specific divisibility properties.