Search results

Create the page "B ny" on this wiki! See also the search results found.

ARML historical results
| [[New York City ARML]] (New York City B) | Westchester City NY

20 KB (2,642 words) - 21:23, 1 June 2024
Mock AIME 1 2006-2007/Problems
<math>ny-p\left\lfloor \frac{ny}{p}\right\rfloor=1</math> ...integers <math>a,b,c</math> where <math>\gcd(a,b,c)=1</math>. Find <math>a+b+c</math>.

8 KB (1,355 words) - 14:54, 21 August 2020
Chicken McNugget Theorem
...ten in the form <math>am + bn</math> for [[nonnegative]] integers <math>a, b</math> is <math>mn-m-n</math>. ...l be called purchasable if there exist nonnegative integers <math>a,b</math> such that <math>am+bn = N</math>.

17 KB (2,748 words) - 19:22, 24 February 2024
1963 IMO Problems/Problem 4
...ite number of solutions in the form <math>(n,n,-\frac{ny}{y+1},-2ny,-\frac{ny}{y+1})</math> where <math>n</math> is a real number and the set is cyclic ( {{IMO box|year=1963|num-b=3|num-a=5}}

3 KB (415 words) - 00:51, 15 September 2023
2004 USAMO Problems/Problem 2
(b) For <math>i,j = 1, \dots, n</math> (not necessarily distinct), <math>a_i - ...math> is in <math>S</math> by (a), <math>0</math> is in <math>S</math> by (b), <math>0 + 1 = 1\in S\Rightarrow 0 - 1 = - 1\in S</math> by (c), and we ca

3 KB (508 words) - 14:23, 17 July 2014
2009 AIME II Problems/Problem 15
...h> be a diameter of a circle with diameter 1. Let <math>A</math> and <math>B</math> be points on one of the semicircular arcs determined by <math>\overl ...th>MA = \frac{\sqrt{2}}{2} \approx 0.707 > \frac{3}{5}</math>, point <math>B</math> lies between <math>M</math> and <math>A</math> on the semicircular a

11 KB (1,862 words) - 21:23, 23 May 2024
Characteristic polynomial
...oot. Then, its closed form solution is of the type <math>x_n = (-1)^n(an + b)</math>. ...monic linear [[homogenous]] [[differential equation]] of the form <math>D^ny +c_{n-1}D^{n-1}y + \cdots + c_1Dy + c_0y = 0</math>, then the characteristi

19 KB (3,412 words) - 14:57, 21 September 2022
2010 AIME I Problems/Problem 13
label("$B$",(255.242,5.00321),NE/2); ...>Y</math> be the foot of the altitude from <math>N</math>, such that <math>NY = 63\sqrt{3}</math> and <math>NU = 21</math>.

10 KB (1,418 words) - 23:05, 20 October 2021
2010 AIME II Problems/Problem 15
pair A,B,C,D,E,M,N,P,Q; B=MP("B",origin, SW);

9 KB (1,523 words) - 15:24, 21 November 2023
Block walking
...ht or down. We start off with some easier means of this problem from A to B by labeling closer distances. Let's label these points with letters. For <math>NY</math> and <math>FY</math> we have to move down or right, and find we have

9 KB (1,228 words) - 21:47, 26 February 2022
2011 IMO Problems/Problem 5
...ies that <math>f(a)|(f(ax + b) - f(b))</math> and therefore <math>f(a) | f(b)</math> (here we used the last observation). integers <math>x</math> and <math>y</math> such that <math>mx = ny + g</math>. Notice that <math>g = mx -

4 KB (825 words) - 01:21, 19 November 2023
1973 AHSME Problems
<math> \textbf{(A)}\ 3\sqrt3\qquad\textbf{(B)}\ 27\qquad\textbf{(C)}\ 6\sqrt3\qquad\textbf{(D)}\ 12\sqrt3\qquad\textbf{( <math> \textbf{(A)}\ 600\qquad\textbf{(B)}\ 520\qquad\textbf{(C)}\ 488\qquad\textbf{(D)}\ 480\qquad\textbf{(E)}\ 400

18 KB (2,788 words) - 13:55, 20 February 2020
Algebraic number theory
In [[mathematics]], algebraic number theory is the study of [[algebraic number|algebraic numbers]] and structures invo ...considering the [[field]] <math>Q[-\sqrt{n}]</math> because then <math>x^2+ny^2=(x+y\sqrt{-n})(x-y\sqrt{-n})</math> is the product of two elements - and

10 KB (1,646 words) - 15:04, 28 May 2020
2008 iTest Problems/Problem 55
label("b",(20,0),S); label("b",(60,0),S);

1 KB (189 words) - 00:19, 13 July 2018
1973 AHSME Problems/Problem 10
<math> ny+z = 1 </math> <math> \textbf{(A)}\ -1\qquad\textbf{(B)}\ 0\qquad\textbf{(C)}\ 1\qquad\textbf{(D)}\ 0\text{ or }1\qquad\textbf{(E)

1 KB (186 words) - 13:58, 20 February 2020
2022 AIME I Problems/Problem 14
...\sim \triangle S_CAB</math> so because <math>BA=B'C</math> and <math>CA=C'B</math>, then <math>S_BB=SBB'</math> and <math>S_CC=S_CC'</math> and <math>S ...<math>NQ</math> and <math>BA</math> is equal to the angle formed by <math>B'C</math> and <math>NQ</math> which is equal to <math>\angle BS_BQ = \angle

16 KB (2,730 words) - 02:56, 4 January 2023
2021 IMO Problems/Problem 4
Using Claim 1 we get <math>\overset{\Large\frown} {TX}</math> symmetric to <math>\ov Using Claim 2 we get <math>TM = QZ, PX = NY.</math>

7 KB (1,196 words) - 10:30, 18 June 2023
Chebyshev polynomials of the first kind
The Chebyshev polynomials of the first kind are defined [[Recursion|recursively]] by <cmath>\begin{align*} T_0(x) &= 1 ...tep, we assume that <math>\cos ((n-1)y) = T_{n-1}(x)</math> and <math>\cos ny = T_n(x)</math>, and we wish to prove that <math>\cos ((n+1)y) = T_{n+1}(x)

10 KB (1,919 words) - 15:24, 26 June 2023
Newton's method
for some <math>b\in\mathbb{Z}</math>. By assumption we know that <math>p(a_0)\equiv 0\pmod{ ''Proof'': Let <math>p(x)=p^ny</math> for <math>y\in\mathbb{Z}_p</math> and <math>p'(x)=p^ku</math> where

13 KB (2,298 words) - 23:34, 28 May 2023
2022 AMC 10A Problems/Problem 1
<math>\textbf{(A)}\ \frac{31}{10}\qquad\textbf{(B)}\ \frac{49}{15}\qquad\textbf{(C)}\ \frac{33}{10}\qquad\textbf{(D)}\ \frac{ ...Diophantine equation <math>(n^2+4)\left(\frac{y}{2}\right)^2-\left(x-\frac{ny}{2}\right)^2=\pm{1}</math>. So for this problem in particular, the denomina

3 KB (413 words) - 12:09, 25 December 2023

Page

Toolbox

Search

Search results