The number nineteen written, in today’s most usual numbering system, like 19, is the last of the digit numbers ending in 9. And one of the four primes between 10 and 20, the others: 11.13 and 17 In Roman numeration XIX is written. Follow 18 and precede 20 in the sequence of natural numbers.
Summary
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- 1 Arithmetic
- 1 Severability
- 2 Numerals
- 3 Algebra
- 4 Geometry
- 5 References and notes
- 6 Sources
- 7 See also
Arithmetic
- It is a prime integer, its only divisors are ± 1, ± 19; As a prime natural number, its only two factors are 1 and 19.
- It is a rational number that can be written as 19k / k for any k integer other than 0.
- Since it is 19 = 4 × 4 + 3, it is not a prime Gaussian integer.
- It is a sum of three squares: 19 = 3 2+ 3 2 +1 2
- It is a positive real number. It is correct to express 19 = 18,999 … [1]
- It is a complex number, 19 = 19 + 0i
- It is a difference of squares: 10 2-9 2 = 19
- It is a difference of cubes: 3 3– 2 3 = 27 -8 = 19
Divisibility
- twin cousin with 17
- A natural number written in the base numbering system 20, like that of the Maya, is divisible by 19, if the sum of the numbers is a multiple of 19.
- Its minimum primitive root is 2 [2]
- The number Au is a multiple of 19 if the algorithm A + 2u is a multiple of 19, as an example: 4655 → 465 + 2 × 5 = 475 → 47 + 2 × 5 = 57 divisible by 19. [3]
Numerals
- binary = 10011
- quaternary 103
- octal 23
- hexadecimal 13
- ternary 21
- quinary 14
- senario 31
- duodecimal 17
- pentadecimal 14
- ordinal: nineteenthor nineteenth
- Partitive: 19th
Algebra
- There are 19 complex roots of 1. Except the real root = 1, the others, or 18 of them are complex numbers. They are called primitive roots.
- The set of nineteenth roots of 1, with the ordinary multiplication of complexes, form a finite and simple abelian group. Any of the primitive roots can generate the rest of the roots.
- The nineteenth power of x + y, this is F (x, y) = (x + y) 19has 20 terms, all of them of absolute degree = 19. Since F (x, y) = F (y, x) is a symmetric polynomial. And since F (tx, ty) = t 19 F (x, y) is a homogeneous polynomial; exploitable features in algebra and analysis.
Geometry
- It is one of the legs of a right triangle, the other leg is 180 and the hypotenuse, 181. Well 19 2+180 2 = 181 2 [4]
