Tags » Arithmetic Progression

Prime-Generating Polynomials

If you haven’t seen it before, the polynomial seems to look like any other. And yet, as Euler noted, this polynomial has a curious property — evaluating at the integers gives a new prime each time: 862 more words

Number Theory

Sums of Squares and Density

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

Analytic Number Theory

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

AS Level

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

Number Theory

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

Derive Formula

Three numbers in A.P. whose sum is a 6-th power

Find three numbers in arithmetical progression whose sum is a 6-th power.

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Number Puzzles

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.

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Number Puzzles