The Cauchy-Davenport Theorem is a result in additive number theory that deals with subsets of integers. It states that if you have two non-empty subsets of integers, A and B , taken from a finite group of integers modulo p (where p is a prime number), the size of the sumset A + B is at least |A| + |B| - 1 . This means that the number of distinct sums you can form from elements of A and B is significant. This theorem highlights the relationship between the sizes of sets and their sumsets, providing insight into how elements combine. It is particularly useful in combinatorial number theory and has applications in various areas, including group theory and combinatorics. The theorem was independently proven by Cauchy and Davenport, which is why it carries both of their names.