Search results
Create the page "P-adic numbers" on this wiki! See also the search results found.
- ...ath> to choose 3 odd numbers. Therefore, the probability of choosing 3 odd numbers is <math>\frac{\binom{1008}{3}}{\binom{2016}{3}}</math>. Simplifying this,2 KB (302 words) - 00:57, 18 October 2024
- ...scu/dp/0817643265/ref=sr_1_1?ie=UTF8&s=books&qid=1204029652&sr=1-1 Complex Numbers from A to... Z] by [[Titu Andreescu]] ...mazon.com/exec/obidos/ASIN/0486638308/artofproblems-20 Geometry of Complex Numbers] by Hans Schwerfdtfeger.24 KB (3,202 words) - 14:33, 13 January 2025
- ...ll triples of positive integers <math>(a,b,c)</math> such that each of the numbers Let <math>\mathbb{R}</math> be the set of real numbers. Determine all functions <math>f:\mathbb{R}\rightarrow\mathbb{R}</math> sat4 KB (709 words) - 14:00, 1 June 2024
- ...ath>x^2 = (-x)(-x) > 0,</math> again by the closure of the set of positive numbers under multiplication. ...l <math>(p,q]</math>, where <math>p</math> and <math>q</math> are rational numbers. Then, <math>p+q</math> can be expressed as <math>\frac{r}{s}</math>, where3 KB (583 words) - 20:20, 2 August 2024
- ...[set]] (usually the set of integers; [[rational]], [[real]] or [[complex]] numbers; but in [[abstract algebra]] often an arbitrary [[field]]). Note that a [[c ...is a constant, the <math>x_i</math> are (not necessarily distinct) complex numbers and <math>n</math> is the degree of the polynomial in exactly one way (not6 KB (1,100 words) - 14:57, 30 August 2024
- ...choose <math>n+1</math> numbers from <math>S</math>, then there exist two numbers such that one is a multiple of the other. ...e <math>b</math> value. These numbers are multiples—if we define the two numbers <math>2^ib</math> and <math>2^jb</math> where <math>i>j</math>, we may mult11 KB (1,986 words) - 18:13, 19 June 2024
- Relatively prime numbers show up frequently in [[number theory]] formulas and derivations: For two relatively prime numbers, their [[least common multiple]] is their product. This pops up in [[Chines2 KB (245 words) - 17:45, 14 October 2024
- ...a_1, \ldots, a_n </math> and <math> b_1, \ldots, b_n </math> be [[complex numbers]]. Then For any real numbers <math>(a_1,a_2,...,a_n)</math> and <math>(b_1,b_2,...,b_n)</math> where <ma13 KB (2,048 words) - 14:28, 22 February 2024
- ...number of factors divisible by a given power of <math>p</math>. Among the numbers <math>1,2,\dots,n</math>, exactly <math>\left\lfloor\frac n{p^k}\right\rflo10 KB (809 words) - 15:40, 17 March 2024
- ...totient function]]. In particular, <math>\varphi(p) = p-1</math> for prime numbers <math>p</math>. In turn, this is a special case of [[Lagrange's Theorem]]. ...to prove [[Euler's Totient Theorem]], if we let <math>S = \{\text{natural numbers relatively prime to and less than}\ n\}</math> <math>\square</math>16 KB (2,660 words) - 22:42, 28 August 2024
- ...ds are particularly well-suited to studying properties of individual prime numbers. From an algebraic perspective, number theory can perhaps best be described ...] are particularly well-suited to studying large-scale properties of prime numbers. The most famous problem in analytic number theory is the [[Riemann Hypothe5 KB (849 words) - 15:14, 18 May 2021
- ...rime number]]s. Now, we can use a [[PIE]] argument to count the number of numbers less than or equal to <math> n </math> that are relatively prime to it. First, let's count the complement of what we want (i.e. all the numbers less than or equal to <math> n </math> that share a common factor with it).5 KB (903 words) - 14:49, 27 July 2024
- ...eal numbers are:<math>1, 2, -23.25, 0, \frac{\pi}{\phi}</math>, and so on. Numbers that are not real are <math>\ 3i</math>, <math>\ 3+2.5i</math>, <math>\ 3+ ...integers and <math>\mathbb{Z}^{-}</math> means negative integers. The real numbers can also be divided between the [[algebraic number]]s and [[transcendental3 KB (496 words) - 22:22, 5 January 2022
- Rule 1: Partition <math>N</math> into 3 digit numbers from the right (<math>d_3d_2d_1,d_6d_5d_4,\dots</math>). The alternating s ...38 - 28 ==> 1210 ==> 121 - 21 ==> 100 ==> 1 NOPE. Works in general with numbers that are relatively prime to the base (and works GREAT in binary). Here's10 KB (1,572 words) - 21:11, 22 September 2024
- ...mposite]] because it is its only factor among the [[natural number|natural numbers]]. ...oof attributed to [[Euclid]] notes that if there are a finite set of prime numbers <math>p_1, p_2, \ldots, p_n</math>, then the number <math>N = p_1p_2\cdots6 KB (1,053 words) - 20:29, 7 January 2025
- ...ts argument is nonnegative. The range is the set of all non-negative real numbers, because the square root can never return a negative value. ...lly we speak about functions whose domain is also a [[subset]] of the real numbers.10 KB (1,761 words) - 02:16, 12 May 2023
- ...esult, they have eight options. So, our total number of two-and-three-free numbers is <math>7 \cdot 8^3 = 3,584</math>. Hence, our final answer is <math>9000 ...the first and third numbers and letters are distinct. The probability the numbers are distinct is <math>\frac{9}{10}</math>, as for every digit of the first8 KB (1,192 words) - 16:20, 16 June 2023
- ...math> people in <math>{{n+1}\choose{k+1}}</math> ways. Now we hand out the numbers <math>1,2,3,\dots,n-k+1</math> to <math>n-k+1</math> of the <math>n+1</math We know since all numbers on LHS are non-negative therefore 0≤N and N is a integer.12 KB (1,993 words) - 21:22, 15 January 2025
- To understand the notion of '''base numbers''', we look at our own [[number system]]. We use the [[decimal]], or base- * [[base numbers/Common bases | Common bases]]4 KB (547 words) - 16:23, 30 December 2020
- ...thcal{P}</math> is defined as the ordered <math>n</math>-[[tuple]] of real numbers <math>\mathcal{P}=(x_0,x_1,\ldots,x_n)</math> such that1 KB (178 words) - 19:34, 6 March 2022