Ads
related to: sum of multiple powers worksheet 1 printableteacherspayteachers.com has been visited by 100K+ users in the past month
- Free Resources
Download printables for any topic
at no cost to you. See what's free!
- Packets
Perfect for independent work!
Browse our fun activity packs.
- Projects
Get instructions for fun, hands-on
activities that apply PK-12 topics.
- Resources on Sale
The materials you need at the best
prices. Shop limited time offers.
- Free Resources
kutasoftware.com has been visited by 10K+ users in the past month
ixl.com has been visited by 100K+ users in the past month
Search results
Results from the WOW.Com Content Network
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.
These symbols are collectively called factorial powers. [ 2 ] The Pochhammer symbol , introduced by Leo August Pochhammer , is the notation ( x ) n {\displaystyle (x)_{n}} , where n is a non-negative integer .
Since a = n(n + 1)/2, these formulae show that for an odd power (greater than 1), the sum is a polynomial in n having factors n 2 and (n + 1) 2, while for an even power the polynomial has factors n, n + 1/2 and n + 1.
In the special case m = 1, the conjecture states that if = = (under the conditions given above) then n ≥ k − 1. The special case may be described as the problem of giving a partition of a perfect power into few like powers. For k = 4, 5, 7, 8 and n = k or k − 1, there are many known solutions. Some of these are listed below.
The sum is taken over all combinations of nonnegative integer indices k 1 through k m such that the sum of all k i is n. That is, for each term in the expansion, the exponents of the x i must add up to n. [1] [a] In the case m = 2, this statement reduces to that of the binomial theorem. [1]
Subset sum problem, an algorithmic problem that can be used to find the shortest representation of a given number as a sum of powers; Pollock's conjectures; Sums of three cubes, discusses what numbers are the sum of three not necessarily positive cubes; Sums of four cubes problem, discusses whether every integer is the sum of four cubes of integers
Ads
related to: sum of multiple powers worksheet 1 printableteacherspayteachers.com has been visited by 100K+ users in the past month
kutasoftware.com has been visited by 10K+ users in the past month
ixl.com has been visited by 100K+ users in the past month