In mathematics and statistics, sums of powers occur in a number of contexts: * Sums of squares arise in many contexts. For example, in geometry, the Pythagorean theorem involves the sum of two squares; in number theory, there are Legendre's three-square theorem and Jacobi's four-square theorem; and in statistics, the analysis of variance involves summing the squares of quantities. * Faulhaber's formula expresses as a polynomial in n, or alternatively in term of a Bernoulli polynomial. * Fermat's right triangle theorem states that there is no solution in positive integers for * Fermat's Last Theorem states that is impossible in positive integers with k>2. * The equation of a superellipse is . The squircle is the case . * Euler's sum of powers conjecture (disproved) concerns situati