Find the multiplicative inverse of a mod n, using 2 different methods. Show your steps in each case a = 4, n = 7 a = 6, n = 13

Q: Sam is laying out patio stones in a triangular pattern. The first row has 2 stones and each row has…

A: Here,  Row 1 has 2 stones Row 2 has 2+2=2(2)=4 stones Row 3 has 2+2+2=2(3)=6 stones . . .

Q: what is the additive inverse of 13

A: Given: The objective is to find the additive inverse of 13. Additive inverse is a number, which when…

Q: Given the recursive formula: an = an-1 + 12 and a1=3. %3D Find the 4th term. O A. 15 ов 3 ос. 27 о…

A: The value of the nth term from the recursive formula can be calculated by evaluating the values of…

Q: Is it possible to raise a positive number b to a power and obtain a negative number? Is it possible…

A: The given statement is " The possibility to raise a positive number b to a power and obtain a…

Q: Find a positive integer less than 8 for x that satisfies x = 720 + 3 (mod 7).

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Q: Two students, Chloe and Jasmine are working on rewriting this expression: V Chloe says this: V = x…

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Q: If mis odd, then m3 - mis divisible by 3.

A: We will check this for m=1 first  0 is divisible  by 3.

Q: Decrypt the message "PYZTP" which was coded using the key f(a) 19a +1 mod 26. Provide full details…

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Q: for 3^800 how can I find the last digits of it by using mods (such as last digit and 2nd last…

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Q: 4x=22(mod10)

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Q: QUESTION 1 Find an integer x between 220 and 260 that satisfies x = 39^123 (mod 41). Your answer…

A: We need to find integer x between 220 and 260 that satisfies x = 39123 mod 41 Clearly , 39 and 41…

Q: Prove that for a positive integer n we have that 33n+3 – 26n – 27 is divisible by 169. - -

A: The given expression is: 33n+3-26n-27 This is to be proved that the expression is divisible by 169.

Q: Give a non-zero numerical counterexample to the following statement: Every multiple of 12 is also a…

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Q: What is two raised to the seventh power?

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Q: Find the product 3/2 (5 /12 + 6/6) and express your answer in the form A/B+ CVD, A, B, C, and D are…

A: Given : 32512 + 66

Q: a. Find the inverse of 17 modulo 97

A: Inverse of 17 modulo 97

Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: Pam is a Disc Jockey. Every week she buys 3 new albums to keep her collection current. She currently…

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Q: What is 5 raised to the power of 1

A: Given :    5 raised to the power of 1

Q: Find the tenth term in the expansion (x+3) 2? Select one:

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Q: Suman and Kashish add and subtract -1 and -6. Suman claims that they can add and subtract the…

A: The given integers are -1 and -6  add them -1+-6=-7 change the order and again add -6+-1=-7 the…

Q: let a = 3^4 7^3 11^2 13^5 and b = 2^6 5^2 7^2 11^3 13^4 Determine the values of (a,b) and [a,b] and…

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Q: 1. Identify the rule that justifies each step to simpl the expression. 2* (-4') a. = 24 (-4) %3D

A: Since we are given with multiple number of question with multiple subparts and our guideline is…

Q: Find to 25 does not require any dividing in order to determine if a number is divisible by 25.

A: The objective of this question is to determine if a given number is divisible by 25 without using…

Q: 2. Create the following tables: (a) Addition table for modulo 7 (b) Multiplication table for modulo…

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Q: Which of the following is additive inverse of 12mod8? a. 90 b. 92 c. 87 d. 66 Ob O C Od

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Q: Number theory

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Q: Find an odd integer o written as an expression using the variable k with the property that when f is…

A: Here we have given a mapping  which proves that both the sets have same cardinality.

Q: Which of the following operations is commutative? Select one: a + b O a. a %3D ab O b. avb = a^b Oc…

A: Only (a) is commutative.   The detailed solution is as follows below:

Q: Q4/ Find the element of GF(2³) then by using the multiplication table find (x+1)-¹ mod (x² + x + 1).…

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Q: what is the additive inverse of 8?

A: Identity elements corresponding to addition is given by 0. So, additive inverse of a is -a  Such…

Q: #5 Find An if n is a positive integer and A = 4 -3 - 2

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Q: True or False. Briefly explain why.  The inverse of 2 modulo 2023 is 22022.

A: We see,       2023 = 7×172    => φ(2023) = 2023(1 - 1/7)(1 - 1/17)                         =…

Q: Then Find inverse of 21 mod 200.

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Q: Write the cycle (1634)(3645) in S7 as a product of disjoint cycles

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