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

Q: 5. Evaluate : 23391 mod 55 (use modular exponentiation)

A: We Know that Modular exponentiation is a type of exponentiation performed over a modulus.

Q: Use the Chinese Remainder Theorem to find a solution to the congruences ´x = 2 mod 10 x = 3 mod 1001…

A: The given system is, x≡2mod10x≡3mod1001x≡3mod9 Chinese reminder theorem: If m1,m2,…,mn are positive…

Q: Consider Z, ={0,1,2,3,4,5,6,7,8,9,10,11} with modular addition, subtraction, and multiplication|…

A:

Q: Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 3. Evaluate : 7644 mod 645 (use modular exponentiation) 4. Evaluate : 1231001 mod 101 (use modular…

A: To evaluate 7644mod 645 74≡466mod 64574161≡466161mod 645 Now,  4662≡436mod 645466280≡43680mod 645…

Q: Modular division can be performed by considering the related multiplication problem. For instance,…

A:

Q: 3. Evaluate : 7644 mod 645 (use modular exponentiation)

A:

Q: For some of the most interesting laws of modular arithmetic (Choose some of your liking, but do…

A: This is a problem of mudular arithmatic.

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?

A:

Q: 35040 MOD 76397. Explain how and why Pollard's p - 1 factorisation method works.

A: Given: p-1 To find: Pollard method

Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?.

A:

Q: Show that an integer N is divisible by 9 if and only if the sum of its digits is divisible by 9

A: Let a=anan-1...a3a2a1 be an integer and S be the sum of the digits. Consider a,…

Q: Show that n22-1 is division by 8, if n is an odd positive integer

A:

Q: (4) Apply the Fast Modular Exponentiation to find 0 < M < 87, where 5015 = M mod 87.

A:

Q: What is the middle term of the expansion (æ² – 4)* - 43750x^8 59080x^8 43500x^8 17920x^8

A: We will find middle term as

Q: Prove by cases that n2−1 is divisible by 3 when n is an integer not divisible by 3.

A: The detailed solution is given below Thank you

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: 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: (2) Use the power property of modular arithmetic and a technique discussed in section 8.4 to…

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Q: Show that n2-1 is division by 8, if n is an odd positive integer

A:

Q: Please explain Modular Exponentiation Find the modular of the following: 5^4358 mod 10

A: This is an easy question and is a consequence of the property of the number 5. The detailed solution…

Q: 5) Using Fermat's little theorem, determine 21998 mod 7. In other words, what is the remainder when…

A:

Q: Solve for x using The Division Algorithim : 937 =x (mod 4)

A:

Q: Decide whether the following binomial congruence has any solutions x2" = 10 mod 103. Use modular…

A: We have to decide whether the following binomial congruence has any solutions or not.…

Q: Do all four problems. 1. Prove that there exists a unique prime number of the form n2 – 4, where n…

A:

Q: 1. What is the remainder when 65544 - 13 is divided by 8?

A:

Q: What is true about the sum of the exponents on a and b in any term in the expansion of (a + b)n?

A: We have the binomial expansion:…

Q: Suppose Alice and Bob have the same RSA modulus n and suppose that their encryption exponents eд and…

A:

Q: it is known that 1x3x5x.x21 + 22x24x26x..x40 = 68a.546.9b3.857.7c5 by using the division algorithm…

A: Given: Let us consider the given 1×3×5×...×21+22×24×26×...×40=68a.546.9b3.857.7c5 Determine the…

Q: Use the modular inverses found in the preceding problem to solve the following congruences, if…

A:

Q: Find an integer that leaves a remainder of 2 whan divided by either 3 or 5, but that is divisible by…

A:

Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?

A:

Q: Problem # 6: Use Interleaved algorithm to solve the following Modular Mu Please show N = 170.60 mod…

A:

Q: A safer system would be to use modular multiplication instead of addition. But if we use modular…

A: The modular arithmetics gives remainder obtained upon division. For example, 26≡1mod 25 means on…

Q: a) Use Fermat’s little theorem to compute 3302 mod 5, 3302 mod 7, and 3302 mod 11.b) Use your…

A:

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

A: We have to solve given problem:

Q: Use modular arithmetic to prove that, if n is an integer not divisible by 5, then n^4 − 1 is…

A:

Q: Answer the following. 1. Find x if 2x309 is divisible by 9 2 Find the canonical prime factorization…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Use the PMI to prove that 6" – 1 is divisible by 5 for every integer n > 0.

A: To prove that 6^n-1 is divisible by 5 for every integer greater that or equals to 0.

Q: Find the mod of (2-4i)^1/2

A:

Q: Find an inverse of 43 modulo 660.

A:

Q: Compute 81^-3/4 without a calculator, writing your answer as a fraction

A: given that, 81-34

Q: Show that n22-1 is division by 8, if n is an odd positive integer

A: If n is a odd positive integer n can be written as   n = 2k+1 by substituting in n2-1 n2-1 =…

Q: Use modular arithmetic to determine the following:  Disregarding a.m or p.m., if it is now 9…

A: If a.m. or p.m. is disregarded, and the time is x o'clock now, then: The time, y hours from now,…

Q: Compute 59^11 mod 13 = You should know how to do this without a calculator by using the modulo…

A:

Q: Show that, given a 7-digit number, where all digits except perhaps the last is non-zero, you can…

A:

Q: Solve (by hand) 6x 5 mod (151) using Pohlig-Hellman. You may use wolfram alpha to do simple…

A: To solve : 6x=5mod151 using Pohlig-Hellman

Q: 1) write the expansion of : (3a + 2b)5,

A: As per bartleby guidelines, for more than one question, only 1st one is to be answered. Please…

Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 8 in.…

A: Let x be the length of a side of the cardboard. Since we are making a square box, the dimensions of…