Compute 59^11 mod 13 = You should know how to do this without a calculator by using the modulo squaring method.

Q: Solve the linear congruence 7x = 13 (mod 19).

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Q: Find the least positive inverse for 97 modulo 660.

A: Theorem used in the solution. For all integers a and b if gcd(a,b)=1 then there exists an integer s…

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: (i)Find the inverse of 5(mod9)     (  ii)Hence or otherwise solve simaltaneous equation…

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Q: Find the primitive roots (mod 17).

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Q: How would I solve for n and m (without a calculator)? Please explain. 5" = 3( mod 97) 5m = 7( mod…

A: to find the value of m , n when 5n≡3 mod 975m≡7 mod 97 (i) we can write 5n≡3 mod 97 as   5n=97s+3…

Q: Find all integer solutions to the equation 23. + 6x2 + x + 6 =1 mod 74. Explain your method and cite…

A: en x3+6x2+x+6 = 1 mod 71

Q: Show that every nonzero residue (mod 17) can be written as a power of 3

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Q: Find all the primitive roots modulo 125.

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Q: Find x such that 1577 =x (mod11), 0sx<11. You must show all the detailed steps

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Q: 3x = 11 (mod 20)

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Q: Find inverse of 55 modulo 243

A: Find inverse of 55 modulo 243

Q: Solve the equation modulo 5.  2x+3=1

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Q: x3-3x2+27 is congruent to 0 (mod 225)

A: Consider the following problem  x3-3x2+27≡0mod 225 Prime factorization of 225 is 32×52 Now,…

Q: If a = 17 (mod 3), then what is the remainder of a when divided by 3? Enter the numerical value.

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Q: Use Fermat’s little theorem to evaluate 9200 mod 19.

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Q: Please explain how to solve: (5 · 17) (mod 8)

A: To solve  (5*17) (mod8) we use the properties of modulo

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

A: Solution...

Q: Use Fermat’s little theorem to find 231002 mod 41.

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Q: The inverse of 3 modulo 7is -2

A: Given statement, The inverse of 3 modulo 7 is -2.

Q: 8. How many positive divisors does 2000= (2^4)(5^3) have?

A: Note: Hey there! Thank you for the question. As you have posted multiple independent questions, we…

Q: Is 17 congruent to 4 modulo 6.

A: 17, when divided by 6, leaves remainder 5

Q: solve 2x 1(mod13)

A: We are given that 2x≡1(mod 13) ⇒2x-1 is divisible by 13. Consider , 2x-1=13m , where m∈Z ⇒x=13m+12,…

Q: Solve x2+3x+2 is congruent to 0 (mod 55)

A: 55=5×11 and gcd(5,11)=1, hence they are co-prime.The given system of equation x2+3x+2≡0mod 55 is…

Q: Find inverse of 65 modulo 243

A: The definition of inverse modulo is: a is said to be the inverse of b modulo p, if ab≡1(mod p)

Q: Solve 10x = 13 (mod 53)

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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: Solve 66x = 111(mod 237).

A: mod of any quantity is positive  i.e ±a  =  a

Q: Use Fermat's little theorem to find 231002 mod 13.

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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: Inverse of 9 modulo 23 is 18

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Q: 2. Find an inverse of 2 modulo 17 that is positive and less than 17.

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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…

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Q: 1. i) Explain why 3 is a primitive root modulo 14 ii) What is log3(11) mod 14?

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Q: Then Find inverse of 21 mod 200.

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Q: 3. Find the residue of 20211202 mod2022 using Euler's Theorem.

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Q: b. 3x = 0 (mod 21)

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Q: 7x =4 (mod 12).

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Q: how do you compute 1.2193 to the 1/3 power?

A: Here we use logarithmic method to find tha solution.

Q: Show 3^1728 ≅ 1mod19 Please do this using the method where you start with 3 to smaller powers and…

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Q: Let x, y ∈Z. Prove that if x≡1(mod 5) and y ≡2(mod5 ), then x^2-y^2≡0(mod 5).  Give 2 examples to…

A: Given, x,y∈ℤ and x≡1mod 5, y≡2mod 5

Q: Inverse of 19 modulo 141 is

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Q: Number theory

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

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Q: How many Gaussian integers have norm 3² . 52. 72 . 294? Try to count them without doing a lot of…

A: To determine how many Gaussian integers have norm 32·52·72·292 Let α=a+ib be an arbitrary Gaussian…

Q: 3) Find 3521 mod 645 by modular exponentiation. You must show your work step by step.

A: Solution: 3521 mod 645

Q: 3 congruent to 1 (mod5) 2 congruent to 3 (mod 7) 5 congruent to 11 (mod3)

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Q: How would you find -88 mod 13?

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