Question 6 Find all whole number solutions of the congruence equation x= 17 mod 7. O (3, 10, 17, 24,...} O {1, 8, 15, 22,...} O {2, 9, 16, 23,...) O {2, 19, 36, 53,...} O (3, 20, 37, 54,...} *

Q: (a) How many three-digit nos. can be formed from the digits 0.1.2.3.4.5 & 6 if each digit can be…

A:

Q: (7) (a) Find the order of a modulo 7 for a = 1, 2, 3, 4, 5, 6.

A:

Q: Statement 1 : 2465 is not a carmichael number Statement 2 : 95 = 55 (mod 2) Statement 1 : True…

A:

Q: You are trying to factor n = 31831 which happens to be the product of 2 primes. Suppose your tions.…

A: An effective way to determine the greatest common divisor (GCD) of two integers is to use the…

Q: Example/Find the nth-term of the following: 1 2 3 4 5 5'7'9'11'13' a) b) 2 4 8 16 32 0! 1!'2! 3!' 4!…

A: To find the n th term of given sequence.

Q: How many permutations π of [10] satisfy π^5 = 1?

A: The given set is 10=1,2,3,…,10. Therefore any permutation π of 10, is bijective function from the…

Q: QUESTION 7. Find the number of permutations of length 9 that satisfy the following conditions: (i)…

A: To find- Find the number of permutations of length 9 that satisfy the following conditions: It…

Q: How many strings of length 12 over the alphabet {a, b, c} have exactly three a's or have exactly…

A: Combinatorics is the field of mathematics in which we deal with counting. Counting is based on the…

Q: Using Chines Reminder Theorem, Solve the congruence x = 4 (mod 13) x = 5 (mod 11) X = 11 (mod 15 )…

A:

Q: 1. Solve the Congruence x^5 ≡ 2 (mod 7)   2. Solve the congruence x^7 ≡ 10 (mod 23)   Show work…

A:

Q: 10. (8 points) Solve 3x 2, (mod 7) or show that no solution exists.

A: Solution: The objective is to find the solutions of 3x≡2 (mod 7)

Q: Prove: The nth Fibonacci number Fn is even if and only if 3 | n.

A: The nth Fibonacci number Fn is even if and only if 3|n.

Q: 17. Classify the definiteness of

A:

Q: 157" =x (mod 11), 0 <x<11

A:

Q: Question 4 Number of solutions of the equation 3x- 2x + 5x² + x + 2 =0 under modulo 5 is/are OA O…

A:

Q: 3. cos0 17 II

A: We have to find out θ value and given is cosθ=-817

Q: QUESTION 4 Find two integers, x, where -3 < x < 12 such that x =4 mod 6 X = and x = YOU MUST SHOW…

A:

Q: 3. From Eq. (1), deduce that U2n-1 2. U2n 2. %D %3D n 2

A: 3

Q: Inverse of 9 modulo 23 is -18 -17 18 17 Windows by

A: Solution: We have to find the inverse of 9 modulo 23. Let x be the required inverse. Then, 9x≡1mod…

Q: (12) (a) Prove that if x € Z and r² is even, then x is even. (b) State and prove an analogous…

A: We prove following statements by using contrapositive method.

Q: 3. Find all solutions to x² + 5 = 0 (mod 245).

A:

Q: Solve by mathematical induction For all integersn> 3, 4(4" – 16) 4 + 4* +4 + .. ……+4" =

A: Solution: The objective is to prove that the given statement using mathematical induction.

Q: 50 Evaluate Σ (5 + 2i) i=1

A: Solution is done in step 2

Q: Suppose x satisfies the three simultaneous congruences X = 4 (mod 5) x = 7 (mod 8) X 10 (mod 11)…

A:

Q: 7. What is the regression equation that would be used to predict Y using X for this problem? 8.…

A:

Q: 2.) Find the check digit (d) for the UPC numbers 0-32692-03012 d

A: 2. The given UPC number is 0-32692-03012-d. We use the first 11 digits 0-32692-03012 to determine…

Q: G I G L 6.1 soup sound ofte for

A: The given number is 1.212121⋯⋯⋯. The number 21 is repeated continuously after the decimal in the…

Q: Show that — ф+1 n=0 ||

A: Given φ is the golden ration satisfying 1φ=φ-1. To prove ∑n=0∞1φn=φ+1 It is known that φ=1+52.

Q: If x – 1 is an even integer, which of the following numbers must be odd? I. x(x - 1) II. 3(x - 1)…

A:

Q: 2.3(i) Find the conjugates, moduli and arguments (to the nearest degree) of the following

A: 2.3(i)   (a). Given,                         3+5i.     To find the conjugate, modulus and argument…

Q: Q13/ A/ Find A-B? * 1 11 B= | 2 15 If A = 2 4 -4 find .3 4] 3

A: Here, A=112434,B=0-12-453

Q: 24. What are the modulus and the principal argument of the -4 + 4i? *

A: Here given complex number as z = -4+4 iThus modules of this complex number is z = (-4)2+42…

Q: (*:') • (":") - () n+1` + 1 a 3 2

A: From ncr formula we can easily derive the answer.

Q: What can you say about the midline or the mindsegment

A: A mid-segment is a line segment which connects the midpoints of two sides of a triangle. The mid…

Q: 5. Prove that the following are irrational: E-2-3', £-12¬!.

A: Expand the given functions and then determine their values. If the values are irrational then the…

Q: Question 2 Solve the linear congruence 19x =7 (mod 90127)

A: We have to Solve given linear congruence by following way.