Find a such that 5= 7* modulo 13.

Q: if b is modulo m and a is another unit with a=b mod m, we say that d is the---------of a modulo m to…

A: As with such a large amount of concepts we are going to see, congruence is straightforward, perhaps…

Q: Let p= 2k +1 be an odd prime number. Show that x* – 1 = (X – 1)(X – 2²) - · (X – k²) mod p.

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Q: Least residue of 8^68 modulo 17

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Q: 6. List all the numbers a such that you can find an a such that ax = 1 modulo 26? call such…

A: 6. For a particular n, all integers which are less than n and co-prime to n, will be invertible…

Q: x^2 ≡ 1 (mod 105)

A: Given: x2≡1(mod 105) To Solve: The given congruence  x2≡1(mod 105)

Q: Find the least residue of 63^9 modulo 10

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Q: Find the smallest positive integer x that solves the congruence: 7x≡5 (mod52)

A: 7x≡5 (mod52)---(1)

Q: Any two integers are congruent modulo .. when they are both even or both odd. Least common multiple…

A: Given a statement

Q: primitive root modulo

A: Given: Value of n=223 in  mod n. To find: Primitive root modulo 223.

Q: Find a primitive root mod 172021

A: If a is a quadratic residue mod 17, then a8≡1 mod 17. Thus order of a≤8. Hence a cannot be a…

Q: Find the least residue of 448 modulo 7

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

Q: What is the least residue of 7162 modulo 17?

A: Multiplication rule for congruencesIf a ≡ b (mod n) and c ≡ d (mod n), thenac ≡ bd (mod n). Power…

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

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Q: Give three elements of the equivalence class of 15 modulo 7

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Q: Find all the primitive roots modulo 125.

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Q: 13. (a) Prove that for each integer a, if a 0 (mod 7), then a #0 (mod 7).

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Q: Determine a positive integer x such that 57x +7 = 78 (mod53).

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Q: Find a primitive root modulo 2 * 19^2022

A: Consider the number n=2×192022. We know that a primitive root of modulo n is an integer g such that…

Q: If the list 7, 10, 5, 9, 11, 12, 6,"3, 8, 4, 2, 1 aj6, consists of powers of g = 7 from 1 to 12…

A: Here we see from the table that 4  Is at location 10 from starting    4=710 mod 13    Taking log7…

Q: 2. Give an example to show that a (mod n). b (mod n) need not imply that a =b

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Q: find the integer x such that 0 < x < 232 and 144x = 4(mod 233). Show your work.

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Q: Suppose that p is a prime number. Given this information prove that if x is an integer such that x^2…

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Q: Number theory

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Q: 122 is congruent to 5 modulo17 ?

A: To check whether -122 is congruent to 5 modulo 17 or not

Q: Find all x EZ221 such that x2 =97 (mod 221).

A: To find : all x∈ℤ221 such that x2≡97mod 221 Pre-requisite : Properties of Legendre symbol - 1. ap=1,…

Q: To Determine the value that 46 is congruent to IN modulo 7

A: Note that, If a and b are integers and n &gt; 0, then a ≡ b (mod n) to mean n|(b − a) and It can be…

Q: (a) Use cases based on congruence modulo 3 and properties of congruence to prove that for each…

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

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Q: find a primitive root mod 172021

A: to find the primitive root of 172021 definition of primitive root let n be a prime integer then g is…

Q: 11. Define conguren ce class es for modulo 4.

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Q: Calculate the least residues modulo 5 of 14, 24, 34, and 44.

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Q: Consider the congruence mod 6 for integers. Z6={[0], [1], [2], [3], [4], [5]}. Prove the sum of an…

A:

Q: 2. Find an inverse of 2 modulo 17 that is positive and less than 17.

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Q: 29 is a primitive root modulo 38? True or False

A: The answer to this question is TRUE.

Q: Prove that if a + x ≡ a +y (mod n), then x ≡y (mod n)

A: I have proved it by using defination of congruent.

Q: 25 Prove that mod 7 5 for all Gindegars and bin b mod 7-6

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Q: 5 is a quadratic non- residue mod 17

A: The quadratic residues mod17 are { 1,2,4,8,9,13,15,16}

Q: Find all integers X satisfying X ≡ 1 mod 6, X ≡ 3 mod 8, X ≡ 7 mod 9

A: First divide 1 i.e. the dividend by 6 i.e. the divisor 1/6 = 0.16667 Then multiple the whole part of…

Q: If a = 3 (mod12) then a does not equal 1 (mod6)

A: a=b mod n if and only if n divides a-b Now, we have that a=3mod 12 We need to show that a≠1mod 6 Let…

Q: Show that : If n is an integer then n is congruent to 0 modulo 4 or 1 modulo 4.

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Q: What is the modulus and argument of -3. Select all that apply

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Q: Find the order of 5 modulo 31.

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Q: Find 2025-3 (mod 212). (Enter the least non-negative integer.)

A: To Find: 2025-3(mod 212) and enter the least non-negative integer.

Q: Partition (Z/19Z)* into equivalence classes determined by the identi- fication of elements of the…

A: According to the given information, it is required to determine the primitive roots modulo 19.

Q: The least positive integer x satisfying 22010 = 3x (mod 5) is

A:

Q: (a) gcd(q, n) = 1 if and only if kq # 0 mod (n) for all 1 < k< n. %3D

A:

Q: Solve for d using Euclid's Extended Algorithm 3d ≡ 1 mod 5200

A: Given 3d≡1 mod 5200 . The objective is to solve for d using Euclid's Extended Algorithm.