Compute 17^7121 (mod 11).

Q: x^2 ≡ 1 (mod 105)

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

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: Find 12 ^– 1(mod 17), the inverse of 12 modulo 17

A: Find an inverse of 12 modulo 17 as follows.

Q: Please show me the necessary steps to prove this. Thanks!Solve the congruence 156x ≡ 402 (mod 570),…

A: In second page " . " means multiplication (in case if you get confused)

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

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Q: Prove that a^561 ≡ a mod 561.

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Q: Compute the 3^201 mod 5.

A: Congruence value

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

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Q: Suppose x^3 = 1 (mod 41). Show that x = 1 (mod 41).

A: Given that: x3≡1mod 41. We have to show that x≡1mod 41.

Q: a be an odd integer. Pro

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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: Find all the primitive roots modulo 125.

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Q: How many 8-bits strings have exactly three 1's?

A: Given that  8 bits strings have exactly three 1 s is

Q: Use Euler's Theorem to compute and reduce 4^1226(mod 35).

A: To solve 41226mod 35 using Euler's Theorem.   Euler's theorem states that if gcda,n=1 then, aϕn≡1mod…

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

A: Solution...

Q: E(n? – vē -n + In *) = = 500 500(501)(1001)] 500(501) + 1000 - In False B) True 6.

A: Let's learn few properties of summation.

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: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

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Q: What is 2 ^32 mod (5)?

A: mod is the function whose output is always positive. mod is represented by .

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: Least residue of 45^37 mod 19 when using Fermats Little Theorem

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Q: Compute (7^3)^161 (mod 250)

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Q: A = [14]. -1

A: Here given A=111-1

Q: Prove that A-B=An(-B) = (-B) – (-A) = −[(-A) U B]. Also, give three expressions for An B and AU B,…

A: Difference of sets: Given two sets A and B, the difference A−B is defined as the set of all elements…

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: Use the Euler Theorem to calculate 17^81(mod 55)

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

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Q: Find the 7-adic expansion of 1/2 up through the 7^3 power

A: jyujhjyukjhjkkhjjghfgf

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

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