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For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 + 1 / 2 , 5/4, and √ 2 are not. [8] The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers.
The symbols for elementary-level math operations. From top-left going clockwise: addition, division, multiplication, and subtraction. Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and division.
Number theory 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."
Frobenius coin problem with 2-pence and 5-pence coins visualised as graphs: Sloping lines denote graphs of 2x+5y=n where n is the total in pence, and x and y are the non-negative number of 2p and 5p coins, respectively.
6 C 3113112211322112211213322112 B 3847.0525419 7 N 111312212221121123222112 C 5014.9302464 8 O 132112211213322112 N 6537.3490750 9 F 31121123222112 O 8521.9396539 10 Ne 111213322112 F 11109.006696 11 Na 123222112 Ne 14481.448773 12 Mg 3113322112 Pm.Na 18850.441228 13 Al 1113222112 Mg 24573.006696 14 Si 1322112 Al 32032.812960 15 P 311311222112
[12] [6] The 2020 Mathematics Subject Classification contains no less than sixty-three first-level areas. [13] Some of these areas correspond to the older division, as is true regarding number theory (the modern name for higher arithmetic) and geometry. Several other first-level areas have "geometry" in their names or are otherwise commonly ...
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