15-1mod 17 (use Fermat theorem)

Q: Prove that 2n32n - 1 is always divisible by 17.

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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: Prove that the analogue of lemma 1.23 is not true for numbers of the form 4n+3 where n is an…

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Q: 1. Explain why Corollary 1 of Theorem 9-7 is true. That is, explain why L1 = L2.

A: Given that ∠1=∠2 is true statementsHint: Major arc; Minor arcand…

Q: Find all solutions of the linear congruence: 9r = 5 mod (14) Define a modular inverse. Find a…

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Q: If A ánd B are two n x n invertible matri hen one of the following is always correct

A: It is given that,  A and B are two n×n invertible matrices.

Q: Suppose that an < bn < Cn for all n, an → L, and cn → L. Show that bn → L.

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Q: Prove that 279,930 is divisible by 7 using Fermat's Little Theorem.

A: We have to prove that 279930 is divisible by 7 using Fermat's Little theorem. The Fermat's little…

Q: 1 = -3.54490 -2, ulgn İhi

A: We use the definition of Gamma function and it's properties to answer the given question.

Q: Show that A= 4 * eye (4) - ones (4, 4) is not invertible: Multiply A* ones (4, 1).

A: We have to show that:  A= 4 * eye (4) - ones (4, 4) is not invertible

Q: Use the Euclidean Algorithm to verify that 935 is an element of U(10192). Then use the reverse…

A: Given number is 935 and the given group is U10192. Now computing the GCD of 935, 10192 using Euclid…

Q: Determine the smallest subring of Q that contains 2/3.

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Q: Suppose A=| use Diagonalization to compute A" 10

A: In the given question we have to find the 10th power of the matrix A s.t A=10-12. Concept: If a…

Q: Find the remainder using Fermat’s Little theorem 452 mod 11.

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Q: Compute the multiplicative inverses of the following (if they exist) usin Using the Euclidean…

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want…

Q: Use nested multiplication algorithm to convert the polynomial 1+2x+3x² into its equivale Newton form…

A: In this question, the nested algorithm to convert the polynomial 1+2x+3x2 into its equivalent Newton…

Q: Prove that 1. 1. 1 + 1x 2'2x 3 1 = 1 – (п — 1) хп + 3 x 4

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Q: Find the multiplicative inverse of the given element.   [11] in Z138

A: To find the multiplicative inverse of the element 11 in Z138

Q: Find the multiplicative inverse of the given element   [9] in Z242

A: To find the multiplicative inverse of the given element 9 in Z242.

Q: A binary linear cyclic block code Ccyc(n, k) has code length n = 14 and generator polynomial g(X) =…

A: ⇒linear block code cyc(n,k)n=14 code word lengthmessage length(k)codding rate(R=kn)=0.4285Minimum…

Q: Show that (AB)¹ = BTA¹ if A = 2 0 2 0 and B = -1 1 15) -3 1 -1 -1 2 2). a

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Q: Evaluate the integral.

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Q: Show that 1+3/ -5 is irreducible which is not prime in ZlV-5]

A: We know that ,  ℤ-5 = a + b-5 / a , b ∈ ℤ We need to show that , 1 + 3-5  is irreducible but not…

Q: The 4th term of an ap is zero. Prove that 25th term of the AP is three times its 11th term

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Q: 1 6 [: 2. Let %3D matnix c (by tnial and erron) Constauct a C (by tnial and eror using anly !,-1 and…

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Q: 4. Find the elements of Zg that have multiplicative inverses.

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Q: Find gcd(2,3+5i) in Z[i]

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Q: Find ln(9.2), using quadratic interpolation, from ln(9.0) = 2.19722, ln(9.5) = 2.25129, ln(10) =…

A: Given ,  ln(9.0) = 2.19722, ln(9.5) = 2.25129, ln(10) = 2.30259, and ln(11) = 2.39790  We have to…

Q: 4. The "divide and average" method, an old-time mthod for approximating the square root of any…

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Q: (i) find gcd(2,3+5i) in Z[i], (ii) show that 3+4i and 4-3i are associates in Z[i] , do all , dont…

A: Solution (i)

Q: The greatest common divisor of two number 1, b(nteger) are. None of the

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Q: Find [7]^-1 in Z55 under multiplication.

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Q: Express 3 cis 133.8° in standard a + bi form.

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Q: an 34an-1 – 289an-2 for n > 3 with initial conditions aj = 68, az = -1734. an

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Q: Only 1 of the next 10 COVID-19 patients will recover. All of the next 10 COVID-19 patients will…

A: Here given that fatality rate of covid 19 here in the Philippines up to date is 1.6%   P =…

Q: Write down the algorithm of Pseudo inverse and also find the solution of given problem using this…

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Q: 7. If x5+1=(x+1)(x²+x+1)(x*+x+1)(x*+x³+x+1)(x*+x³+x²+x+1) are the factors of x'5+1, find the…

A: We know that gx is a generator polynomial for a linear cyclic code of length n if and only if gx…

Q: Show that Zn has a nonzero nilpotent element if and only if n is divisibleby the square of some…

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Q: Produce an example of a subset of 1R³ that is Closed under addition, but not closed under scalar…

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Q: Only 0.1% of the individuals in a certain population have a particular disease (an incidence rate of…

A: Given: P (disease) = 0.001 P (Positive | disease) = 0.90 P (negative | do not disease) = 0.90

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

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Q: 4. Modular Inverse Compute an inverse of 70 modulo 39 by running the extended Euclidean algorithm…

A: This is a problem of Number Theory.

Q: Prove that tim 51

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Verify that transposition errors of adjacent digits lxi I and lXi- 1 will be detected in a bank…

A: On the contrary, assume that xi-xi+1≠5. Let identification number for bank have eight digits. That…

Q: 1 -1 on 1 of the product matri חר

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Q: Theorem 4.6 (Fundamental Theorem of Arithmetic) Every positive integer n can be written as the…

A: Given fundamental theorem of arithmetic: Every positive integer n can be written as the product of…

Q: Let Z, = { 0, 1, 2, 3, 4, 5, 6 } where each x e Z, is a least residue when an integer is divided by…

A: (4) Given that ℤ7=0, 1, 2, 3, 4, 5, 6, where each x∈ℤ7 is a least residue when an integer is divided…

Q: (a) Prove that the product of two even permutations is even.

A: please post the multiple question separately. Here I answered 1st question only as per our policy.