Compute 17^7121 (mod 11).

Q: Is there a solution to x^2 - 9x + 17 = 0 mod 73?

A: The given in this question is a quadratic equation in the form of x2-9x+17=0, and the objective is…

Q: Use Fermat's little theorem to find the least residue of 8^70 modulo 23

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Use Fermat's Little Theorem to compute 51990 mod 7.

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Q: congruences 4* = 13 (mod_17) and 54 (mod 19).

A: Given congruences are: 4x≡13mod 175x≡4mod 19 We have to solve the given exponential congruences.

Q: Prove that a^561 ≡ a mod 561.

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Q: Compute the 3^201 mod 5.

A: Congruence value

Q: Compute 2021^2021(mod 1000). The answer is 421. Show the work.

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Q: How could we calculate the congruences 10^x ≡ 243 mod 19^2 with 14x^15 ≡17 mod 19. The answer of mod…

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

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Q: Use four terms of Newton's binomial expansion to approximate 11.

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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: 1. Explain why you can find 25^1202 mod 61 quickly without using the binary modular exponentiation…

A: To apply format theorem: Format theorem: Let “P” be a prime and suppose that then, aP-1≡1 mod  P As…

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

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Q: Find the inverse of 35 under mod 233(if exixts), by using Euclid's Algorithm?

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Q: Compute 386 mod 89.

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Q: solve the quadratic congruence 7x^2 - 8x +4 = 0 (mod 17)

A: The given problem is to solve the given quadratic congruence equation 7x2-8x+4 = 0(mod 17)

Q: solve for x^2 = 1 mod 8 and x^2 = 1 mod 10

A: Solution...

Q: Compute 25200 mod 27.

A: As 25 is coprime to 27, by Euler's theorem, we see        25φ(27) ≡ 1 (mod 27)  Now,        φ(27) =…

Q: 75 (mod 46)

A: Take a number and modulo with 46

Q: Use Hensel’s Lemma and Chinese Remainder Theorem to find all solutions to x^2 + 3x + 17 ≡0 (mod 300)

A: Introduction: Hensel’s Lemma is a powerful tool in number theory that allows us to lift solutions of…

Q: show that 2 is a primitive root mod 3^e for all e>=1

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Q: Compute 177121 mod 11.

A: To find 177121 = mod 11

Q: A = [14]. -1

A: Here given A=111-1

Q: we have 1529 MOD 83 = 2 Find the inverse to 2 by using the Euclid's algorithm

A: The given expression is 1529 mod 83=2. We have to find the inverse of 2 by using Euclid's algorithm.

Q: Solve 10x = 13 (mod 53)

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Q: Use the Euclidean Algorithm to determine if 7^-1(mod 20) exists.

A: To determine if 7-1mod 20 exists, using Euclidean Algorithm.

Q: Compute the following modular exponents. 11^6mod14=   11^ 5 mod 15 =. 3^3mod5 =

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Q: Compute 9 x 10999,999,999,999,999,999 (mod 13).

A: To Compute: 9×10999,999,999,999,999,999 (mod 13)

Q: Find a such that 5= 7* modulo 13.

A: Given: 5≡7xmodulo13. The objective is to find the value of x.

Q: 3 . Use the baby-step giant-step algorithm to find h, k such that 2^h ≡ 7 (mod 53), 2^k ≡ 9 (mod…

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Q: ind e so that 23^e = 1(mod 21)

A: Here we use Euler’s phi theorem: Let n be a positive integer and a an integer relatively prime with…

Q: Find all solutions of quadratic congruence x^2+85x+2=0(mod401)

A: We follow the method of completing the squares of the equation x^2+85x+2. Note that 85 is odd so we…