Category:Examples of Use of Sum of Two Odd Powers

This category contains examples of use of Sum of Two Odd Powers.

Let $\F$ be one of the standard number systems, that is $\Z, \Q, \R$ and so on.

Let $n \in \Z_{\ge 0}$ be a positive integer.

Then:

$\ds a^{2 n + 1} + b^{2 n + 1}$

$=$

$\ds \paren {a + b} \sum_{j \mathop = 0}^{2 n} \paren {-1}^j a^{2 n - j} b^j$

$\ds $

$=$

$\ds \paren {a + b} \paren {a^{2 n} - a^{2 n - 1} b + a^{2 n - 2} b^2 - \dotsb - a b^{2 n - 1} + b^{2 n} }$

Subcategories

This category has only the following subcategory.

The following 3 pages are in this category, out of 3 total.