The Norman identity is a mathematical formula that relates the sums of powers of integers to the coefficients of polynomials. Specifically, it expresses the sum of the n -th powers of the first m integers in terms of binomial coefficients. This identity is useful in combinatorics and number theory, providing a way to calculate these sums efficiently. In its simplest form, the identity can be written as a polynomial involving the binomial coefficients C(n, k), where n is the power and k represents the index of summation. The identity highlights the connections between algebra and combinatorial counting, making it a valuable tool for mathematicians.