1800 BCE) contains a list of " Pythagorean triples", that is, integers ( a, b, c ). The earliest historical find of an arithmetical nature is a fragment of a table: the broken clay tablet Plimpton 322 ( Larsa, Mesopotamia, ca. In particular, arithmetical is commonly preferred as an adjective to number-theoretic. (The word " arithmetic" is used by the general public to mean " elementary calculations" it has also acquired other meanings in mathematical logic, as in Peano arithmetic, and computer science, as in floating point arithmetic.) The use of the term arithmetic for number theory regained some ground in the second half of the 20th century, arguably in part due to French influence. I self learned number theory (first for Olympiad preparation and then just for fun). Malik,Edition, Table of Contents, Syllabus, Index, notes,reviews and ratings and more, Also Get Discounts,exclusive offers & deals on books (Paperback & Hardcover) for students and Professionals. By the early twentieth century, it had been superseded by "number theory". Malik Book Online shopping at low Prices in India. The older term for number theory is arithmetic. One may also study real numbers in relation to rational numbers, for example, as approximated by the latter ( Diophantine approximation).
Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion ( analytic number theory). Seeing the title, one expects the book to begin with the usual elements arithmetic operations, prime numbers, unique factorization and so on. Integers can be considered either in themselves or as solutions to equations ( Diophantine geometry). André Weil, one of the leading mathematicians of the 20th century, wrote a book he called Basic Number Theory. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences-and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). 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 integer-valued functions. This Ulam spiral serves to illustrate it, hinting, in particular, at the conditional independence between being prime and being a value of certain quadratic polynomials. The distribution of prime numbers is a central point of study in number theory.
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