In arithmetic and algebra, the seventh power of a number n is the result of multiplying seven instances of n together.
The sequence of seventh powers of integers is: In the archaic notation of Robert Recorde, the seventh power of a number was called the "second sursolid".
[1] Leonard Eugene Dickson studied generalizations of Waring's problem for seventh powers, showing that every non-negative integer can be represented as a sum of at most 258 non-negative seventh powers[2] (17 is 1, and 27 is 128).
All but finitely many positive integers can be expressed more simply as the sum of at most 46 seventh powers.
[4] The smallest number that can be represented in two different ways as a sum of four positive seventh powers is 2056364173794800.