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: 2. Euclidean Algorithm Use the Euclidean algorithm to find gcd(12345, 678).

A:

Q: 46. Find the order of 7 modulo 172.

A:

Q: b"=1 (mod n) is valid for which of the following pair (b,n) (9.7,1729) (97,1729) (-97,1729)…

A: Answer

Q: Find all solutions to 17r = 14 (mod 21).

A:

Q: What is the value of Y after solving the following expression? Y= Not 15 Mod 5 = 24/6 And 50 / 2 >=…

A:

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: 2n-1 b) Prove that if , r #1 (mod 2"), then n is even.

A: Given that x2n-1≢1mod2n . The objective is to show that n is even. The x2n-1≢1mod2n can be written…

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: 31 = 10 mod 3. :Select one True False

A:

Q: How many square roots of 3 (mod 1001) are there? (Hint: 1001 = 7 * 11 * 13)

A:

Q: If n is a positive integer, explain why each prime in the factorization 'n² must occur an even…

A: (a) Let p be a prime number that occurs in the prime factorization of n2.   This implies that p…

Q: (135+136) 123 =1 (mod 10) Select one: True O False

A:

Q: rd. 17. Show that every decimal palindromic integer with an even number of digits is divisible by…

A:

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

A:

Q: (73 – 98)(mod 3) = (mod 3)

A: GIiven, a expression using modulo function.

Q: Find all integer solutions to the equation 23. + 6x2 + x + 6 =1 mod 74. Explain your method and cite…

A: en x3+6x2+x+6 = 1 mod 71

Q: If x108 = 1(mod 109) then possible value of x is (а) 108 (b) 218 (c) 109 (d) None c Select one: • bx…

A: Find the possible value of x If x108= 1(mod109).

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

A:

Q: Simplify the following expressions by hand and show your work: 23^421 mod 31 57^2024! mod 43…

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: 2. Determine the highest power of 5 that divides each of the following positive integers. a) 112,250…

A:

Q: 2) Find 281171 + 171281 (mod 12)

A:

Q: (d) (e) (f) Assume that a 15 = 1 Find the value of ord41a. mod 41 and a #1 mod 41. How many…

A: As per the question we have to find : ord41(a) , where a15 ≡ 1 mod 41 but a ≠ 1 mod 41 total number…

Q: how do i use Euler's thm to find the value? 3242 mod 385

A:

Q: (3) If today is Thursday what day of the week will it be 31 days from today? (4) If it is currently…

A:

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: Determine the cube root of (3 + j4). ound-off the modulus to 3 decimal places, the angle to the…

A: Cube root of (3+4j)

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: If AC 3x-11 and BD 2x+ 10, find the values of X and the length of BD. B E. D C 2+10, find the values…

A: Given figure, Given that : AC=3x-11 and BD=2x+10 we have to find the value of x and length of BD.

Q: Compute the value of the expression: [72 ·(-65) + 211] mod 7

A: To calculate the below modulo.  72⋅−65+211mod  7

Q: Secton 5.1 Excerciser # 4

A:

Q: It is given that 3023 is prime, and 3023 = 2(1511) +1 where 1511 is also prime. (a) How many…

A:

Q: ) If 112021 =r (mod 13), Find out the value of r. Justify the answer with your work.

A:

Q: X = 17 (mod 21) X= - ) 8 Cmod 25

A:

Statements and Logic

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