The remainder when aa is divided by 77 is 22 and the remainder when bb is divided by 77 is 55. (So a mod 7=2 b mod 7=5) Find: (a+a) mod 7 (a+b) mod 7 (3a) mod 7 (2b) mod 7

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: Suppose b is any integer. If b mod 12 = 5, what is 6b mod 12? In other words, if division of b by 12…

A: Given b is an integer such that b mod12=5 To find the value of  6b mod12

Q: Suppose b is any integer. If b mod 12 = 7, what is 8b mod 12? In other words, if division of b by 12…

A: Given b mod 12= 7  To find 8b mod 12

Q: What are the FOUR values of x that will satisfy: x ≡ 4 mod 5 & x ≡ 3 mod 7 please show your…

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Q: How do I prove this:  Let d ∈ N and let a, b ∈ Z. Prove or give a counterexample: If a 6≡ 0 (mod d)…

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Q: Find all integer solutions satisfying all the equations given. 5x =1 mod 39 3x =1 mod 25 4x =1 mod…

A: Concept :.   *   ax =6 mod n                           g (d (a,n) = d (let)…

Q: 1. How many solutions( mod 419) does x = 186 mod 419 have? (Show your work!) 2. How many solutions (…

A: Given: x2≡186 mod 101 We need to solve x2≡186 mod 101 and how many solution exists.

Q: Let be a prime number. Stating any results that you use, deduce that xº-1 = (x – 1)(x – 2) · . · (x…

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Q: Two great mathematicians who have contributed greatly in the field of modular arithmetic are Swiss…

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Q: 1. Find the value for q given: (a) 39 = 4( mod 5) (b) -43 = 1( mod 4)

A: Note: Hi! Thank you the question, As per the honor code, we'll answer the first question since the…

Q: Suppose b is any integer. If  b mod 12 = 5,  what is 6b mod 12? In other words, if division of b by…

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

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Q: 2n3 + 3n2 +n ≡ 1 (mod 6) Select one: True False

A:

Q: 2x = 4 (mod 8) a. has no solution b. has infinite solutions c. has a unique solution modulo 8 which…

A: Here 2x≡4 (mod 8). Hence 2x=4+8k, for some integer k. Dividing by 2, x=2+4k, for some integer k.…

Q: 4. Using your work from the earlier parts or independently find: (a) mod 8 (b) + mod 23 17 (c) mod 7

A: Given

Q: 5) Using Fermat's little theorem, determine 21998 mod 7. In other words, what is the remainder when…

A:

Q: 3. First solve for q: (a) 143 = 1( mod 2) (b) Rewrite 143 as the product of 11 x 13 and show that…

A: Consider the given information: a=q m+ r Where a= dividend , q=quotient, m=mod , and r=remainder. To…

Q: Euler's Theorem states that if n is a positive integer and a is relatively prime to n, then ar(n) =…

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

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Q: True or False For arbitrary integers a and b, a ≡ b(mod n) if and only if a and b do not have the…

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Q: divisionless mod" where x mod y is computed in steps. One step is to consider y in the form of 2a -…

A: I have answered this question in step 2.

Q: The preceding part of the problem proves the reverse implication unless n = p2 where p is a prime.…

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Q: Use your work from problem 2 and the method used in the example at the end of Lecture 16 to solve…

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Q: Consider the equation 2x + 1 = 0 mod n. For which n are there no solutions? one solution? multiple…

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Q: State whether True or False: If A and B are integers and A ≡ 3 (mod 3) and B ≡ 2 (mod 6) then A+B ≡…

A:

Q: What is the result of: 6(40 – 13) (mod 11) The result is 8

A: Given 6(40-13)(mod 11)

Q: what is the particular solution to the difterential equahion y's +e, subject to y l) = 4e %3D why…

A: Given differential equation is y'=-yx+ex we can write it as y'+yx=ex I.F. is I.F.=e∫1xdx=elogx=x…

Q: Suppose b is any integer. If b mod 12 = 7, what is 5b mod 12? In other words, if division of b by 12…

A:

Q: Suppose that a and b are integers, a ≡ 7 (mod 19), and b ≡ 5 (mod 19), Find the integer c with 0 ≤ c…

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Q: which one will give a solution of [6,13] a)4x is identical to 3 mod 7 b)9x is identical to 11 mod…

A: which one will give a solution of [6,13]

Q: One step is to consider y in the form of 2a - b. When y is 125, what are a and b? Find: A = ? B =…

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Q: Suppose that 3x ≡ 2 (mod 5). Find the remainder when x is divided by 5; in other words, compute x…

A: ANSWER :

Q: (b) Give an example of a composite integer n such that the congruence x =1 (mod n) pas more than two…

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Q: Find the mod of (2-4i)^1/2

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Q: duce the expression for u to 2(5 ,Y = (1+5P) +4 (mod 2p - 1) or simply, to 2u, = 1+5P-1(mod 2p - 1).…

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Q: 9. a. Solve xQ + Q – 4 = 3Q + 5 (mod 2Q), where Q = 2 b. Find the quotient and remainder when Q is…

A: 9. a) Given congruence is xQ+Q-4≡3Q+5mod 2Q where Q=2 Using the value Q=2 in the given congruence…

Q: Suppose n is a large odd number. You calculate 2(n-1)/2 = k (mod),  where k is some integer k is not…

A: Given that 2n-12≡kmodn Take the square on both sides, 2n-12≡kmodn2n-12·2≡k2modn2n-1≡k2modn (a) The…

Q: 3. If a = b (mod n), prove that gcd(a, n) = gcd(b, n). 4. (a) Find the remainders when 250 and 4165…

A: Given below the detailed solution

Q: Which are true for modulo 12? 1.) Does 5x ≡ 6 mod 12 have a solution? How many? 2.) Does 4x ≡ 6 mod…

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Q: 3x is congruent to 2 mod 13

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Q: Compute 22 mod 3, 24 mod 5, 26 mod 7.  What do you notice?  Does Fermat predict your answers? (If…

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Q: Find all solutions to the congruence 10x≡5 mod 15 (b) Prove that 7 divides 32n+1+ 2n+2for any…

A: In  (a) we use the extended Euclidean algorithm to solve the problem. In (b) we use the mathematical…

Q: Find all integers, n, where -15 ≤≤ n ≤≤ 15 which make 15 ≡≡ n mod 4  (4 points) Show all your work:…

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Q: The equation 21x = 49 (mod 77) has: O no solution modulo 77 only 7 non-congruent solutions modulo 77…

A: Solution

Q: Fermat's Little Theorem tells us that if p is prime and a is an integer not divisible by p, then…

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Q: Use the baby step, giant step method to solve 2k = 7 mod 13

A: The objective is to find the value for k from the given equation 2k=7mod13 using baby step method…

Q: How would you find -88 mod 13?

A: