Erdős–Fuchs theorem

The Erdős–Fuchs theorem is a result in number theory, specifically concerning sequences of positive integers. It states that if you have a sequence made up of positive integers, and the sum of the reciprocals of the integers in the sequence is infinite, then certain conditions can determine the density of the sequence within the positive integers. In simpler terms, it helps mathematicians understand how "spread out" the numbers in a particular sequence are, especially when considering infinitely many fractions formed from those numbers. This theorem is useful in various areas of mathematics, including combinatorics and number theory.