4. (i) Using the fauct that 187 = 11 · 17, show that 21к—174 ноd 187. This shows that 187 fails the base 2 primality test. (iї) Соmpute 21911 mod 1911. Use Fermat's little theorem and hand calculations. Does 1911 pass or fail the base 2 primality test? n primo fuotorim Vou ua. of 1011

Q: Compute √27 using once False Position method with x₁ = 1 and x = 2. A 1,69 B 1,84 1,93 1,78

A: We have to compute 275 using the method of False position once where xl=1 and xu=2

Q: Evaluate: 3135 mod 59. (Note that 3519 = 1000112) %3D

A: General form is given by: memod n Here, e=35, m=31 and n=59 Step1) Write the binary form of e 1 0 0…

Q: True or false: If p is an odd prime, then (p-1)! + 2^(p-1) congruent 0(mod p). Justify your answer.

A: p is an odd prime.

Q: find x, where x= 9753 (mod 120) and -120<x<0

A: Ans: -87

Q: 6. A. Show that 81 – x²dx : 81n %3| 4

A: According to company rule we can answer only first question and rest can be reposted

Q: 2. Express (5)"x5 as a Single power with positive t exponents.lyou must show work.)

A:

Q: 2 +3" En=D0 %3D 5n+1 Select one: O True O False 5/56

A:

Q: Find all values of x (using congruent notation) for 35x ≅ 3 (mod 89)

A:

Q: Suppose x^3 = 1 (mod 41). Show that x = 1 (mod 41).

A: Given that: x3≡1mod 41. We have to show that x≡1mod 41.

Q: Find in modulus-argument form [(1+iv3)³/ E-1+i)²]°.

A:

Q: 3. Which of the following integers are divisible by 3? Of those that are, which are divisible by 9?…

A:

Q: (a) Show that, for any odd prime p > 5, 1 if p = 1, –5 (mod 12) (주) -1 if p= -1,5 (mod 12)

A:

Q: Determine all possible digits to place in the square that make the statement true. If none exists,…

A: Given that 40234156. We have to fill in the square for which whole number is divided by 9.…

Q: Rum: sum o fust n natural To werify the Am :- numbers usarg the fermula and equare grid Precedure: -…

A: To verify the formula for sum of n natural numbers using the square grid.

Q: Find the unit digit of 11140 (a) 1 (b) 4 (c) 6 (d) 8 (e) None of these b.

A: The unit digit of a number, abcd is d . For example, the unit digit of the number 1234 is 4. If 0 is…

Q: 5. Find the highest power of 2 that divides each of the following integers. a) (101111110)2 b)…

A: The decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n): decimal =…

Q: True or False: 3^208= 3 mod 53.

A:

Q: A) Find the multiplicative inverse of 4 modulo 13. B) Use your answer from (a) to solve 4x = 5 (mod…

A: a) To find the multiplicative inverse of 4 modulo 13. b) To solve the linear congruence 4x≡5mod 13.

Q: Determine the number of primitive roots modulo 23.

A: Solution

Q: Solve x21 ≡ 6 mod 7

A: If p is a prime number then xp-1≡1(mod p) for all x∈ℤ~pk  where pk denotes multiples of p . Suppose…

Q: 9999 =9 (mod 10) Select one: O True O False

A: Any number with 9 in ones place when multiplied with itself will give 1 in ones place and when it is…

Q: 2. What are the prime factors for the below numbers and arrange them in a canonical form. a. 17 b.…

A:

Q: Sort this permutation [5 213 4] into identity permutation [123 4 5]. Check what's the number number…

A: The permutation is nothing but the arrangement of objects in different orders. If we permute a set…

Q: One of the striking properties of Fibonacci numbers is that gcd(Fm, Fn) = Fd, (*) where d = gcd (m,…

A: 1. We see,        F9 = 34    [Fibonacci series : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,. . . . . ]…

Q: 1) Simplify the following expressions : 15 а) 2z Зх — 7 b) ( 6x + 5)2 13х + 9 6х + 5 x2 + 4x x2- 14x…

A:

Q: Simplify (15-54)(mod 4). (15-54)(mod 4) =(mod 4)

A: Simplify          (15 - 54)(mod 4)

Q: 5. Find the highest power of 2 that divides each of the following integers. a) (101111110)2 b)…

A: Given: (101111110)2 (1010000011)2 (111000000)2 (1011011101)2 Which of these is divisible by 3

Q: TRUE or FALSE: 1. There is no integer n such that 4 | (n^2-2) 2. The GCD of all prime numbers is 1.…

A:

Q: Q020 til Jistil= a Evaluate +Re(

A: We need to evaluate the integral, ∫z+i=2z+i2020+Re(z) dz. So, ∫z+i=2z+i2020+Re(z)…

Q: Question 8 -37 = 3 (mod 5) True False A Moving to another question will save this response.…

A:

Q: there are 3 square roots of 0 when we work mod 45 give all 3 of them

A:

Q: Simplify (98 +31)(mod 7).

A: To simplify (98+31)(mod7), first perform the addition inside the parentheses and then find the…

Q: sigib-wal Jangsal bis batuseanss od nao tada ats 27. Write each of the number in expanded form into…

A: In Hindu-Arabic standard form of an expression 2×103+5=2×1000+5=2005

Q: It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a…

A:

Q: 1/25/22, 11:47 AM What value is equivalent to the expression shown? 32.43. 576 1152 288 756 Which…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.