PDF4PRO ⚡AMP

Modern search engine that looking for books and documents around the web

Example: air traffic controller

Math 127: Chinese Remainder Theorem

math 127: Chinese Remainder TheoremMary Radcliffe1 Chinese Remainder TheoremUsing the techniques of the previous section, we have the necessary tools to solve congruences of the formax b(modn). The Chinese Remainder Theorem gives us a tool to consider multiple such , let s just ensure that we understand how to solveax b(modn).Example that 3x 7 (mod 10) on our previous work, we know that 3 has a multiplicative inverse modulo 10,namely 3 (10) 1. Moreover, (10) = 4, so the inverse of 3 modulo 10 is 33 27 7 (mod 10).Hence, multiplying both sides of the above equation by 7, we obtain3x 7 (mod 10) 7 3x 7 7 (mod 10) x 49 9 (mod 10)Hence, the solution isx 9 (mod 10).Example that 3x 6 (mod 12). oh. This time we don t have a multiplicative inverse to work with. So what to do?Well, let s take a look at what this would mean. If 3x 6 (mod 12), that means 3x 6 is divisibleby 12, so there is somek Zsuch that 3x 6 = 12k. Now that we re working in the integers, wecan happily divide by 3, and we thus obtain thatx 2 = 4k.

Example 5. Use the Chinese Remainder Theorem to nd an x such that x 2 (mod5) x 3 (mod7) x 10 (mod11) Solution. Set N = 5 7 11 = 385. Following the notation of the theorem, we have m 1 = N=5 = 77, m 2 = N=7 = 55, and m 3 = N=11 = 35. We now seek a multiplicative inverse for each m i modulo n i. First: m 1 77 2 (mod5), and hence an inverse to m 1 ...

Fullscreen Download
Loading..

Tags:

  Chinese, Math, Theorem, Remainder, Chinese remainder theorem, Remainder theorem, Math 127

Information

Domain:

Source:

Link to this page:

Please notify us if you found a problem with this document:

Spam in document Broken preview Other abuse

Transcription of Math 127: Chinese Remainder Theorem

Documents from same domain

G V;E

www.math.cmu.edu

We define its dual G = (V ;E )as follows: There is a vertex f correspond-ing to each face f of G. There is an edge e corresponding to each edge e of G. f and g are joined by edge e iff edge e is on the boundary of f and g. Cut edges yield loops. Theorem 1 (a) G is planar.

  G v e

Math 228: Kuratowski’s Theorem - CMU

www.math.cmu.edu

this is the case. Note that u cannot have degree 1, since otherwise, it must be that v is a cut vertex (see Figure 3). Hence, u must have another neighbor in G, say w. Let us consider the graph Gnfug. Notice that this graph is still connected, by the de nition of 2-connectedness, and hence there exists a path in Gnfugbetween w and v.

  Degree, Math, Theorem, Kuratowski, Connectedness, Math 228, Kuratowski s theorem

Vita PO-SHEN LOH March 2018 - Department of …

www.math.cmu.edu

Patent P. Loh, L. Hamilton, and R. Li, Adaptive learning system using automatically-rated applications problems and pupils, U.S. Patent App. #15/435930, led Feb. 17, 2017

  2018, Problem

International Journal of Heat and Mass Transfer

www.math.cmu.edu

598 W.-T. Wu et al./International Journal of Heat and Mass Transfer 112 (2017) 597–606. C 10, C 10 and h c are constants related to the effect of temperature, and m is the power-law exponent. Also, in the above equation, we have separated the dependency of the shear viscosity on the

  Heat, Transfer, Mass, Heat and mass transfer

21-241: Matrix Algebra { Summer I, 2006 Practice Exam 2

www.math.cmu.edu

Replacing b1;b2 by 2, ¡6 respectively in the echelon form we obtained above, we can write out the solution y = (6 ; 4) T . This is to say, x = 6u 1 + 4u 2 , so the coordinate

  Practices, Summer, Matrix, 2006, Algebra, Matrix algebra summer i, 2006 practice

Variations on Cops and Robbers - math.cmu.edu

www.math.cmu.edu

The cops win and the game ends if eventually a cop steps into the vertex currently occupied by the robber; otherwise, i.e., if the robber can elude the cops indefinitely, the robber wins. The cop number of G, denoted by c(G), is the minimum number of cops needed to win on

  Variations, Pocs, Robber, Variations on cops and robbers

Optimizing Jungle Paths in League of Legends

www.math.cmu.edu

Optimizing Jungle Paths in League of Legends 21-393 Final Project Fall 2013 Taylor Caligaris Isa Daher Andrew Kharma William Veer . 1 Introduction League of Legends (LOL) is a popular videogame internationally. It is classified as a multiplayer online battle arena game (MOBA).During these games two teams composed of five players each ...

  Optimizing, Jungle, League, Path, Optimizing jungle paths in league

Differential Calculus - Carnegie Mellon University

www.math.cmu.edu

210 CHAPTER 6. DIFFERENTIAL CALCULUS As for a real-valued function, it is easily seen that a process pis contin-uous at t∈ Dompif it is differentiable at t.

  Differential, Calculus, Differential calculus

INTRODUCTION TO RANDOM GRAPHS - CMU

www.math.cmu.edu

Random graphs were used by Erdos [285] to give a probabilistic construction of˝ a graph with large girth and large chromatic number. It was only later that Erdos˝ and Renyi began a systematic study of random graphs as objects of interest in their´ own right. Early on they defined the random graph G n;m and founded the subject.

  Introduction, Graph, Random, Introduction to random graphs

Math 127: Propositional Logic

www.math.cmu.edu

understanding of propositional logic. 2.3 Negation Our last basic logical operator is negation, a fancy way to say \not." De nition 5. Let p be a proposition. The negation of p, denoted :p, is a proposition that is true when p is false, and false when p is true. This operator is fairly straightforward: it simply takes the opposite truth value ...

  Logic, To say

Related documents

11.Remainder and Factor Theorem (A)

irp-cdn.multiscreensite.com

The Remainder Theorem If is any polynomial and is divided by then the remainder is . If = 0, then is a factor of . We apply the Remainder Theorem to obtain the remainder when %( ’) = 2 4 + 7’-+2’ 9 was divided by (2’ + 3). By the Remainder Theorem, the remainder is %A−4-B. %F− 3 2 G = 2(− 3 2)4 +7(− 3 2)-+2(− 3 2)+ 9 %F− 3 2 ...

  Theorem, Remainder, Remainder theorem

3.2 The Factor Theorem and The Remainder Theorem

www.shsu.edu

Theorem 3.5.The Remainder Theorem: Suppose pis a polynomial of degree at least 1 and cis a real number. When p(x) is divided by x cthe remainder is p(c). The proof of Theorem3.5is a direct consequence of Theorem3.4. When a polynomial is divided by x c, the remainder is either 0 or has degree less than the degree of x c. Since x cis degree

  Theorem, Remainder, Remainder theorem

The Chinese Remainder Theorem - luc.edu

gauss.math.luc.edu

By solving this by the Chinese remainder theorem, we also solve the original system. (The solution is x 20 (mod 56).) Of course, the formula in the proof of the Chinese remainder theorem is not the only way to solve such problems; the technique presented at the beginning of this lecture is actually more general, and it requires no mem-orization.

  Theorem, Remainder, Remainder theorem

The Chinese Remainder Theorem - homepages.math.uic.edu

homepages.math.uic.edu

Chinese Remainder Theorem tells us that there is a unique solution modulo m, where m = 11 ⋅ 16 ⋅ 21 ⋅ 25 = 92400. We apply the technique of the Chinese Remainder Theorem with k = 4, m 1 = 11, m 2 = 16, m 3 = 21, m 4 = 25, a 1 = 6, a 2 = 13, a 3 = 9, a 4 = 19, to obtain the solution. We compute z 1 = m / m 1 = m 2 m 3 m 4 = 16 ⋅ 21 ⋅ ...

  Chinese, Theorem, Remainder, Chinese remainder theorem

The Remainder Theorem - cdn.kutasoftware.com

cdn.kutasoftware.com

The Remainder Theorem Date_____ Period____ Evaluate each function at the given value. 1) f (x) = −x3 + 6x − 7 at x = 2 2) f (x) = x3 + x2 − 5x − 6 at x = 2 3) f (a) = a3 + 3a2 + 2a + 8 at a = −3 4) f (a) = a3 + 5a2 + 10 a + 12 at a = −2 5) f (a) = a4 + 3a3 − 17 a2 + 2a − 7 at a = 3 6) f (x) = x5 − 47 x3 − 16 x2 + 8x + 52 at ...

  Theorem, Remainder, Remainder theorem

THE CHINESE REMAINDER THEOREM

kconrad.math.uconn.edu

The Chinese remainder theorem can be extended from two congruences to an arbitrary nite number of congruences, but we have to be careful about the way in which the moduli are relatively prime. Consider the three congruences x 1 mod 6; x 4 mod 10; x 7 mod 15:

  Chinese, Theorem, Remainder, Chinese remainder theorem

Section 4.3 - The Chinese Remainder Theorem

zimmer.csufresno.edu

Thus the remainder is 10 when 7×8×9×15×16×17×23×24×25×43 is divided by 11. Exercise 12: Use Fermat’s Little Theorem to find the least positive residue of 2 10 6 modulo 7. Solution: Note that 10 6 = 6(166,666)+4.

  Theorem, Remainder, Remainder theorem

The Remainder Theorem and Bounds Date Period

cdn.kutasoftware.com

Find the remainder when f (x) is divided by x k. 5) f ( x ) x x x x x x k

  Theorem, Remainder, Remainder theorem

Remainder Theorem and Factor Theorem - mrsk.ca

mrsk.ca

Remainder Theorem and Factor Theorem Remainder Theorem: When a polynomial f (x) is divided by x − a, the remainder is f (a)1. Find the remainder when 2x3+3x2 −17 x −30 is divided by each of the following: (a) x −1 (b) x − 2 (c) x −3 (d) x +1 (e) x + 2 (f) x + 3 Factor Theorem: If x = a is substituted into a polynomial for x, and the remainder is 0, then x − a is a factor of the ...

  Theorem, Remainder, Remainder theorem, Theorem remainder theorem

Related search queries

Remainder, Theorem, Remainder Theorem, Chinese remainder theorem, Theorem Remainder Theorem