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- For any finite set <math>X</math>, let <math>| X |</math> denote the number of elements in <ma where the sum is taken over all ordered pairs <math>(A, B)</math> such that <math>A</math> and <math>B</math> are s9 KB (1,471 words) - 16:41, 1 February 2024
- Let <math>\mathbb Q_{>0}</math> be the set of all positive rational numbers. Let <math>f:\mathbb Q_{>0}\to\mathbb R</m ...>M</math> be the number of beautiful labelings, and let N be the number of ordered pairs <math>(x, y)</math> of positive integers such that <math>x + y \le n<4 KB (696 words) - 05:43, 17 February 2021
- ...</math> and two sides with lengths <math>4</math> and <math>10</math>. The set of all <math>s</math> for which <math>\tau(s)</math> is nonempty, but all t .../math> denote the number of elements in <math>S</math>. Find the number of ordered pairs <math>(A,B)</math> such that <math>A</math> and <math>B</math> are (n8 KB (1,429 words) - 14:31, 26 February 2024
- Over all ordered triples of positive integers <math>(a,b,c)</math> for which <math>a+b+c^2=a ...exists an integer <math>n\ge2020</math> such that when the elements of the set <math>\{1,2,\ldots,n\}</math> are sorted lexicographically from least to gr8 KB (1,298 words) - 18:32, 7 January 2021
- ...pairs <math>(t,b')</math> have one-to-one correspondence, we consider the ordered pairs <math>(t,b')</math> instead. The requirements become <math>t\equiv8-b Consider the set of all <math>2^{8+6}=2^{14}</math> possible choirs that can be formed. For8 KB (1,183 words) - 00:36, 27 May 2024
- ...</math> by <math>2</math> square centered at <math>(3x, 3y)</math> for all ordered pairs of integers <math>(x, y).</math> ...th>(0, 0)</math>. (minus the teleportations) Since counting the complement set is easier, we'll count the number of <math>4</math>-step paths such that Fr17 KB (2,801 words) - 07:29, 4 November 2022
- Find the number of ordered positive integer triplets <math>(a,b,c)</math> such that <math>a</math> eve ...ith imaginary part greater than <math>0</math>. Let <math>T</math> be the set of all <math>9</math>th primitive roots of unity with imaginary part greate7 KB (1,149 words) - 17:16, 15 December 2020
- ...y)</math> which both <math>x</math> and <math>y</math> are elements in the set <math>\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\}</math>, <math>x</math> and < What can be a description of the set of solutions for this: <math>x^{2}+y^{2}=|2x+|2y||</math>?15 KB (2,366 words) - 17:45, 19 September 2021
- ...> such that <math>m</math> and <math>n</math> are positive integers in the set <math>\{1, 2, ..., 30\}</math> and the greatest common divisor of <math>2^m To count the ordered pairs <math>(m,n),</math> we perform casework on the number of factors of <7 KB (1,212 words) - 15:54, 15 April 2024
- ...i\sqrt{3}}{2},</math> where <math>i = \sqrt{-1}.</math> Find the number of ordered pairs <math>(r,s)</math> of positive integers not exceeding <math>100</math ...e sequence <cmath>3,4,5,a,b,30,40,50</cmath> is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression9 KB (1,520 words) - 19:06, 2 January 2023
- ...y)</math> which both <math>x</math> and <math>y</math> are elements in the set <math>\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\}</math>, <math>x</math> and < What can be a description of the set of solutions for this: <math>x^{2}+y^{2}=|2x+|2y||</math>?14 KB (2,226 words) - 23:39, 12 September 2021
- ...y)</math> which both <math>x</math> and <math>y</math> are elements in the set <math>\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\}</math>, <math>x</math> and < We can begin by converting all the elements in the set to Modular of <math>5</math>. Then, we realize that all possible elements t1 KB (186 words) - 02:05, 15 June 2021
- ...n \leq 1000</math>. Let <math>M_n</math> be the number of integers in the set Find the number of elements in the set7 KB (1,225 words) - 03:05, 4 May 2024
- ...ts</math>, <math> a_m</math> be <math> m</math> different numbers from the set <math> \{1, 2,\ldots, n\}</math> such that for any two indices <math> i</ma ...ger <math>k</math>, let <math>f(k)</math> be the number of elements in the set3 KB (545 words) - 14:01, 19 April 2024
- Consider the set of complex numbers <math>z</math> satisfying <math>|1+z+z^{2}|=4</math>. Th How many ordered pairs of positive real numbers <math>(a,b)</math> satisfy the equation15 KB (2,168 words) - 05:11, 4 February 2024
- Let S be a finite set of positive integers. Assume that there are precisely 2023 ordered pairs (x, y) in S × S so that the product xy is a perfect square. Prove th431 bytes (70 words) - 11:48, 1 November 2023
- Find the number of [[elements]] in the [[set]] Finding the no. of [[elements]] in the [[set]] means finding no. of [[ordered pairs]] of (<math>a</math>, <math>b</math>)2 KB (299 words) - 02:48, 4 May 2024
- For any finite non empty set X of integers, let max(X) denote the largest element of X and |X| denote the number of elements in X . If N is the number of ordered368 bytes (72 words) - 01:02, 27 October 2023
- Note that there are only <math>3</math> primes in the set <math>\{1,2,3,4,5,6\}</math>: <math>2,3,</math> and <math>5</math>. Thus if ...in this scenario because there is only one factor of <math>5</math> in the set. Because of this, having <math>j</math> fives in our prime factorization of13 KB (2,194 words) - 19:10, 18 December 2023
- ...ts in the plane, no three of which lie on the same line. At most how many ordered triples of points <math>(A,B,C)</math> in <math>R</math> exist such that <m878 bytes (151 words) - 02:42, 3 January 2024
