Integer solutions refer to the values of variables in an equation that are whole numbers, including positive numbers, negative numbers, and zero. For example, in the equation x + y = 5, the pairs of integers like (2, 3) or (0, 5) are considered integer solutions because they satisfy the equation without resulting in fractions or decimals. Finding integer solutions is a common problem in areas such as algebra and number theory. Techniques like graphing or using Diophantine equations can help identify these solutions. Integer solutions are important in various applications, including computer science, cryptography, and optimization problems.