*Lagrange’s Four Square Theorem* (Lagrange, 1770) is the well-known result that every positive integer can be written as the sum of four integer squares. This was strengthened by Legendre’s 1797-1798 proof of the similar-sounding… 1,275 more words

## Tags » Arithmetic Progression

#### Sums of Squares and Density

#### Arithmetic Progression OCR AS Level May 2009

The tenth term of an arithmetic progression is equal to twice the fourth term. The twentieth term of the progression is 44.

(i) Find the first term and the common difference. 86 more words

#### Units Groups and the Infinitude of Primes

Throughout, we take as a complex subring (with unity). In this article, we’ll be interested in natural analogues of Euclid’s proof of the infinitude of the primes (i.e. 1,157 more words

#### Sum of 1 to n, n² or n³

We will derive summation of series with increasing difficulty.

Lets derive the simplest series summation formulas,

To derive a formula to this series consider adding the same series with all numbers reversed, that is and so on till i.e, check the following equations, 157 more words

#### Triangle(a,b,c); a^2, b^2, c^2 and cot of interior angles are in A.P.

Let be the sides of triangle such that are in A.P.

Prove that the cotangent of the interior angles are also in A.P.

#### To make {(a+b-c), (a+c-b), (b+c-a)} all squares, (a,b,c) in AP

Find three numbers in arithmetic progression such that

(1)

(2)

(3)

, ,

where the common difference is

(1) ………..

(2) ………..

(3) ………..

, , are in A.P., that is, … 69 more words