 5.6.1: 5 = 11 + 14. Show by computing each expression that 25 mod 6 = (11 ...
 5.6.2: 395 = 129 + 266. Show by computing each expression that 395 mod 4 =...
 5.6.3: 262 = 74 + 188. Show by computing each expression that 262 mod 13 =...
 5.6.4: Prove that for any integers x and y, (x + y) mod n = (x mod n + y m...
 5.6.5: 486 = 18 # 27. Show by computing each expression that 486 mod 5 = (...
 5.6.6: 7067 = 191 # 37. Show by computing each expression that 7067 mod 8 ...
 5.6.7: Prove that for any integers x and y, (x # y) mod n = (x mod n # y m...
 5.6.8: Prove that for any integers x and y, (x # y) mod n = (x mod n # y m...
 5.6.9: Using the hash function of Example 51, which of the following Socia...
 5.6.10: Find a set of five numbers in the range 30, 2004 that cause 100% co...
 5.6.11: Using a hash table of size 11 and the hash function x mod 11, show ...
 5.6.12: Using the completed hash table from Exercise 11, compute the averag...
 5.6.13: When a computer program is compiled, the compiler builds a symbol t...
 5.6.14: Explain what problem can arise if an item stored in a hash table is...
 5.6.15: A disadvantage of hashing with linear probing for collision resolut...
 5.6.16: Generalize the answers to Exercise 15 to explain why using linear p...
 5.6.17: Decode the following ciphertext messages that were encoded using a ...
 5.6.18: Using a Caesar cipher, encode the following plaintext messages. a. ...
 5.6.19: The following ciphertext message is intercepted; you suspect it is ...
 5.6.20: The following ciphertext message is intercepted; you suspect it is ...
 5.6.21: Use the algorithm of Example 53 to compute the 1bit circular left ...
 5.6.22: Use the algorithm of Example 53 to compute the 1bit circular left ...
 5.6.23: Consider a short form of DES that uses 16bit keys. Given the 16bi...
 5.6.24: Describe how to perform a 1bit right circular shift on a 4bit bin...
 5.6.25: Using RSA encryption/decryption, let p = 5 and q = 3. Then n = 15 a...
 5.6.26: Why is the RSA encryption of Exercise 25 a poor choice?
 5.6.27: Using RSA encryption/decryption, let p = 5 and q = 11. Then n = 55 ...
 5.6.28: Using RSA encryption/decryption, let p = 23 and q = 31. Then n = 71...
 5.6.29: a. All n people in a group wish to communicate with each other usin...
 5.6.30: Computer users are notoriously lax about choosing passwords; left t...
 5.6.31: a. The ISBN10 of the sixth edition of this book is 071676864C w...
 5.6.32: A bookstore placed an order for 2000 copies of Harry Potter and the...
 5.6.33: Given the 11 digits 02724911637, compute the check digit for the UP...
 5.6.34: A taxpayer wants his tax refund to be deposited directly to his ban...
 5.6.35: a. Write an algorithm to decompose a fourdigit integer into the on...
 5.6.36: The following quilt image is based on addition modulo n for what va...
 5.6.37: Prove that if x y (mod n) and c is a constant integer, then xc yc (...
 5.6.38: This exercise explores the converse of Exercise 37, which is the is...
 5.6.39: If p is a prime number and a is a positive integer not divisible by...
 5.6.40: Let m1, m2, , mn be pairwise relatively prime positive integers (th...
 5.6.41: The remaining step in the proof of the RSA algorithm is to show tha...
Solutions for Chapter 5.6: The Mighty Mod Function
Full solutions for Mathematical Structures for Computer Science  7th Edition
ISBN: 9781429215107
Solutions for Chapter 5.6: The Mighty Mod Function
Get Full SolutionsSince 41 problems in chapter 5.6: The Mighty Mod Function have been answered, more than 4257 students have viewed full stepbystep solutions from this chapter. Chapter 5.6: The Mighty Mod Function includes 41 full stepbystep solutions. Mathematical Structures for Computer Science was written by Patricia and is associated to the ISBN: 9781429215107. This textbook survival guide was created for the textbook: Mathematical Structures for Computer Science, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(DÂ» O.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.
I don't want to reset my password
Need help? Contact support
Having trouble accessing your account? Let us help you, contact support at +1(510) 9441054 or support@studysoup.com
Forgot password? Reset it here