You are trying to factor n = 2288233. Suppose you discover that 8805252 = 2 ,  20572022 = 3, and 6485812 = 6 (mod n). Use this information to factor n

Q: Number theory

A: Here, x6+1 is reducible in the field mod 2 (when x = 1). So,  the reduction of  x6+1 will be either…

Q: Find the answer of -16 mod 5

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Q: find x, where x= 9753 (mod 120) and -120<x<0

A: Ans: -87

Q: Fermat's "Little" Theorem states that whenver n is prime and a is an integer, a"-l = 1 = 1 mod n a)…

A: Given a =463 and  n=953 We need to find x such that                   463952 ≡ x (mod 953).

Q: Use Eulers thm to find , 7଼8003 mod 1000

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Q: Find the value of 3443 mod 23 4 16 O 3

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Q: Find the inverse of 31 modulo 73

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Q: y = 3x - 5 mod 26 СРHТXT

A: Let us consider the equation y≡ax+b(mod 26) To decrypt the message  Convert the equation in terms…

Q: What are the coefficients of æ5000 and æ4999 in the simplified expansion of (5æª – 2)²2021?

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Q: How to find 85307 (mod 739)?

A: To make it simple , divide power by 4 then solve .

Q: 2. Determine x >0 for each case: 5903 = x (mod 60), 17342 =r (mod 5).

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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: For which odd primes p is 5 a square modulo p?

A: As we know that  a is Quadratic residue mod p if and only if   a(p-1) /2 =1 mod p . If p and q are…

Q: Find the least residue of  -5 -46 modulo 14.

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

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Q: 3x = 11 (mod 20)

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Q: 2) Find 281171 + 171281 (mod 12)

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Q: If you randomly pick integers from 1 to 200, how many would you have to pick to ensure that at least…

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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: Find integers X, E > 2 such that XE = X (mod 74329). How does this illustrate a potential problem in…

A: Given :           E ≥ 2 such that XE ≡ X (mod 74329).   To find integer X.

Q: Find an integer A so that: A79 = 7 (mod 277) Please solve step by step thanks!

A: Given an equation. Let's solve for A.

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: Suppose you are using the fast method to compute xe mod N, where x=23, e=101 and N=515. You have…

A: We will find out the required value.

Q: Find the integer that satisfies: 30x4 ≡ 12 (mod 67)

A: Given the expression is, 30x4≡12mod 67

Q: Find s e Z with 0ss< 13, so that s = 127+300(mod 13). Your work should show a method that does not…

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Q: Find the order of 4 modulo 49.

A: Evaluate order of 4 modulo 49.

Q: Solve for x: 34⁵⁰≡3x (mod26 )

A: Let us consider the equation ax≡b (mod n) is a modulo equation  where x is the solution of the…

Q: 2. Find all solutions, or show there are none, to the congruence X78 = 5 (mod 19)

A: By Fermat little theorem x18≡1mod19. Therefore, x4×18+6≡x6mod19 or x78≡x6mod19.

Q: determine n between 0 and 16 such that (405)(777) is congruent n(mod 17)

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Q: Determine the remainder of 102020 modulo 2020 and the remainder of 102020 modulo 2021.

A: solution 104≡1920(mod2020)…

Q: Using Fermat's theorem, find 3201 mod 11.

A: Euler's Theorem states that for any natural  number n, we  have  aϕ(n)≡1(mod n) where ϕ(n) denotes…

Q: Find a number that is less than 1740719 which is congruent to 577 modulo 1279 and congruent to 317…

A: Given, a number that is less than 1740719 which is congruent to 577 modulo 1279 and congruent to 317…

Q: Find all solutions for 10x = 14 mod 1008

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Q: Construct the addition and multiplication table for Z4 (Note that, both operations are mod4)

A: We have to solve given problem:

Q: 7x =4 (mod 12).

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Q: Find an inverse of 43 modulo 660.

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Q: A.)Many printed airline tickets contain a 10-digit document number followed by a check digit. The…

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Q: O Find 5675 (mod 19

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Q: ere they want me to find a div m and a mod m when a = −33, m = 67. How I solved, I divided -33 into…

A: To find a div m and a mod m when a = −33, m = 67. Given information:  a = -33 m = 67

Q: Use Euler's theorem to evaluate: 9 (mod 14) for a =1446.

A: Euler's theorem:- If gcd a,n=1 then aϕn≡1mod n. here ϕn is Euler's function. The number of integer…

Q: 13, Let (n, e) = (16504217646971, 78893) be Alice's public key, where e represents the encryption…

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Q: Find the least residue of 99! (Mod 101)

A: Introduction: In number theory, Wilson's theorem is a very significant theorem. It states that for…

Q: Calculate 433940584939 mod 988027. Show how do obtain your claimed solution.

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Q: Find the order of 5 modulo 31.

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Q: how did they get 9x^2 from (x^4)/(5x^2)mod11 ?

A: Use of z11[x],

Q: a) Find a, b if a + 2b = 116 mod 9 and 2a + b = -62 mod 7. b) Write the prime factorization of…

A: Note: We are allowed to solve one question/ three subparts at a time so kindly upload remaining…

Q: Find a number a between 0 and 86 such that 71122 = a (mod 87).

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Q: Find all the integers that satisfy 140x = 133 (mod 301).

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