What is the least residue of 7162 modulo 17?

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: Evaluate (3459874 * 457832 * 34568) mod 10. Box in your final answer. Remember to show all work.

A: As we know  a*b mod n = (a mod n)*(b mod n)

Q: Prove that the order of 3 modulo 19 is a divisor of 18.

A:

Q: 2. Find a primitive root modulo 41.

A: We have to find a primitive root of 41.

Q: Test2

A: We know that2198=2128×264×24×22Also we have22≡4(mod 397)24≡16(mod 397)28≡256(mod…

Q: Y OU (a) Find the least residue of 639 modulo 10. (b) Use Fermat's little theorem to find the least…

A:

Q: Find 8081 mod 11.

A:

Q: Find the least residue of 448 modulo 7

A: Given problem is : Find the least residue of 448 modulo 7

Q: Show that every nonzero residue (mod 17) can be written as a power of 3

A:

Q: Find all the primitive roots modulo 125.

A:

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

A:

Q: Find the inverse s of -1959 modulo 979 such that 0 <s< 979

A:

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

A:

Q: Find the least positive integer n that satisfies the congruence 7 ^128 congruent to n (mod13)

A: Given, 7128≡nmod 13 Find the value of n that satisfies the above congruence.

Q: Prove a2 = c² (mod n), assuming that a, c and n are integers with n > 1 and that a = c (mod n)

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: Secton 5.1 Excerciser # 4

A:

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

A:

Q: Calculate 21212 (mod 9211), reducing it to a positive number less than 9211. Show your calculations.…

A: The objective of this question is to calculate the modulo of 21212 by 9211. The modulo operation,…

Q: What is the order of 3 modulo 101? Is 3 a primitive root modulo 101?

A: Here we have to find the order of 3 modulo 101 and find if 3 is the primitive root modulo 101 or…

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: whether 2 is a primitive root modulo 19. Please state the reason.

A:

Q: (d) 357 862 193 = (mod 943). (e) 5327 6135 7139 2187 5219 . 1873 = (mod 8157). (Hint. After each…

A: ...

Q: Compute (1001 mod d) for d = 2, 3,..., 10.

A:

Q: Show that y = x (mod p) leads to -y = -x (mod p).

A: