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2. Primes in arithmetic progression - Wikipedia

   en.wikipedia.org/wiki/Primes_in_arithmetic...

   In number theory, primes in arithmetic progression are any sequence of at least three prime numbers that are consecutive terms in an arithmetic progression. An example is the sequence of primes (3, 7, 11), which is given by a n = 3 + 4 n {\displaystyle a_{n}=3+4n} for 0 ≤ n ≤ 2 {\displaystyle 0\leq n\leq 2} .

3. Arithmetic progression - Wikipedia

   en.wikipedia.org/wiki/Arithmetic_progression

   Arithmetic progression. An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression. For instance, the sequence 5, 7, 9, 11, 13 ...

4. Dirichlet's theorem on arithmetic progressions - Wikipedia

   en.wikipedia.org/wiki/Dirichlet's_theorem_on...

   In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is also a positive integer. In other words, there are infinitely many primes that are congruent to a modulo d.

5. Number theory - Wikipedia

   en.wikipedia.org/wiki/Number_theory

   Mathematics. Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." [1]

6. AM–GM inequality - Wikipedia

   en.wikipedia.org/wiki/AM–GM_inequality

   Visual proof that (x + y)2 ≥ 4xy. Taking square roots and dividing by two gives the AM–GM inequality. [1] In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same ...

7. Roth's theorem on arithmetic progressions - Wikipedia

   en.wikipedia.org/wiki/Roth's_Theorem_on...

   Roth's theorem on arithmetic progressions (infinite version): A subset of the natural numbers with positive upper density contains a 3-term arithmetic progression. An alternate, more qualitative, formulation of the theorem is concerned with the maximum size of a Salem–Spencer set which is a subset of [ N ] = { 1 , … , N } {\displaystyle [N ...

8. National Council of Educational Research and Training

   en.wikipedia.org/wiki/National_Council_of...

   NCERT. Website. www .ncert .nic .in. National Council of Educational Research and Training ( NCERT) ( Hindi: राष्ट्रीय शैक्षिक अनुसंधान और प्रशिक्षण परिषद) is an autonomous organisation of Ministry of Education, the Government of India. Established in 1961, it is a ...

9. AOL Mail

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