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Problem 6. The number 65537 is prime, and 3 is a primitive root. Show what computation...
7.23 Theorem. Let p be a prime congruent to 3 modulo 4. Let a be a natural number with 1 a< p-1. Then a is a quadrut...
7.23 Theorem. Let p be a prime congruent to 3 modulo 4. Let a be a natural number with 1 a< p-1. Then a is a quadrutic residue modulo pif and only ifp-a is a quadratic non-residue modulo p. 7.24 Theorem. Let p be a prime of the form p odd prime. Then p 3 (mod 4). 241 where q is an The next theorem describes the symmetry between primitive roots and quadratic residues for primes arising from odd Sophie...
ame: . (10 points) Let p > 3 be any prime number. (a) Show that p...
ame: . (10 points) Let p > 3 be any prime number. (a) Show that p mod 6 is equal to 1 or 5 (b) Use part (a) to prove that pe - 1 is always a multiple of 24.
Question1: Alice and Bob use the Diffie–Hellman key exchange technique with a common prime q =...
Question1: Alice and Bob use the Diffie–Hellman key exchange technique with a common prime q = 1 5 7 and a primitive root a = 5. a. If Alice has a private key XA = 15, find her public key YA. b. If Bob has a private key XB = 27, find his public key YB. c. What is the shared secret key between Alice and Bob? Question2: Alice and Bob use the Diffie-Hellman key exchange technique with a common...
Problem 3. (i) Show that the Taylor series expansion of the function , with center at 1, is for -1
Problem 3. (i) Show that the Taylor series expansion of the function , with center at 1, is for -1<1 ii) Explain why the function Log z is analytic in the disk l:-1 iii) For each point z with :-1< 1 consider the straight line segment C starting at 1 and ending at z. Evaluate dz. Hint: You do not need to do any computation. Note that Logz is an antiderivative of 1/z in the disk :-1<1.) (iv) Integrate each...
Problem 2 (25 Pts,) Root locus: A proportional only action is controlling a plant with unity feedback. The plant transfer function is: 6 G)+ G+2)(6 +3) a. Draw the poles of G (s) in below figure...
Problem 2 (25 Pts,) Root locus: A proportional only action is controlling a plant with unity feedback. The plant transfer function is: 6 G)+ G+2)(6 +3) a. Draw the poles of G (s) in below figure b. How many asymptotes does the root locus plot of the above transfer function has? c. What angles do the asymptotes make with the positive real axis in the s plane? d. At what point do the asymptotes intersect on the real axis? e....
Problem 1: Implement an algorithm to generate prime numbers. You will need to implement the following...
Problem 1: Implement an algorithm to generate prime numbers. You will need to implement the following ingredients (some of them you developed for earlier assignments): 1. A method to generate random binary numbers with n-digits (hint: for the most significant digit, you have no choice, it will be 1; similarly, for the least significant digit there is no choice, it will have to be 1; for all other position, generate 0 or 1 at random) 2. A method to compute...
This problem is concerned with evaluating some improper integrals. In particular you will use an ...
This problem is concerned with evaluating some improper integrals. In particular you will use an improper integral over an interval of infinite length to evaluate an integral of a function not defined at one end point. This will involve a special function「which arises in many applications in the sciences. a. Evaluate Jo (log z) dr. b. Explain how you would evaluate Jr*(log x)7 dr, but do not actually compute it. Would your method work if the exponent'8, were replaced by...
CH, NH, or HS up ng a number without giving appropriate attention to organizir Part A...
CH, NH, or HS up ng a number without giving appropriate attention to organizir Part A - Organize the data Since volume and produre are inversely related, we can make some assumptions about initial and final states using the data provided. We can also identity initial and fi finding trigger words in the language of the problem. Look for words like "First, initially." or "originally to describe initial states and result or after for final states. What volume would a...
6. For a positive real number z, the difference 1.-z- is called the fractional part of r. Given a...
6. For a positive real number z, the difference 1.-z- is called the fractional part of r. Given arbitrary positive real numbers a and b, state a condition in terms of the fractional parts of and that is necessary and sufficient for la + bl = lal + Ibl Prove that this equation is true if and only if your condition holds. 7. Evaluate 10002+4 23k+5 k- 2 algebraically and simplify as much as possible. You ust show all steps....
Problem 5 answers: 3x coverage = 256.3114 30x coverage = 2563.1143 answer problem 6 pls Problem...
Problem 5 answers:
3x coverage = 256.3114
30x coverage = 2563.1143
answer problem 6 pls
Problem 5 (1 point): Now let's think about sequencing reads and read length. How do could you determine how many reads you need from a given genome at a certain level of coverage? You can do this by multiplying the length of a genome by coverage divided by read length. As defined in a formula we have L(C/R) where L = genome length, c =...
7.23 Theorem. Let p be a prime congruent to 3 modulo 4. Let a be a natural number with 1 a< p-1. Then a is a quadrutic residue modulo pif and only ifp-a is a quadratic non-residue modulo p. 7.24 Theorem. Let p be a prime of the form p odd prime. Then p 3 (mod 4). 241 where q is an The next theorem describes the symmetry between primitive roots and quadratic residues for primes arising from odd Sophie...
ame: . (10 points) Let p > 3 be any prime number. (a) Show that p mod 6 is equal to 1 or 5 (b) Use part (a) to prove that pe - 1 is always a multiple of 24.
Problem 3. (i) Show that the Taylor series expansion of the function , with center at 1, is for -1<1 ii) Explain why the function Log z is analytic in the disk l:-1 iii) For each point z with :-1< 1 consider the straight line segment C starting at 1 and ending at z. Evaluate dz. Hint: You do not need to do any computation. Note that Logz is an antiderivative of 1/z in the disk :-1<1.) (iv) Integrate each...
Problem 2 (25 Pts,) Root locus: A proportional only action is controlling a plant with unity feedback. The plant transfer function is: 6 G)+ G+2)(6 +3) a. Draw the poles of G (s) in below figure b. How many asymptotes does the root locus plot of the above transfer function has? c. What angles do the asymptotes make with the positive real axis in the s plane? d. At what point do the asymptotes intersect on the real axis? e....
This problem is concerned with evaluating some improper integrals. In particular you will use an improper integral over an interval of infinite length to evaluate an integral of a function not defined at one end point. This will involve a special function「which arises in many applications in the sciences. a. Evaluate Jo (log z) dr. b. Explain how you would evaluate Jr*(log x)7 dr, but do not actually compute it. Would your method work if the exponent'8, were replaced by...
CH, NH, or HS up ng a number without giving appropriate attention to organizir Part A - Organize the data Since volume and produre are inversely related, we can make some assumptions about initial and final states using the data provided. We can also identity initial and fi finding trigger words in the language of the problem. Look for words like "First, initially." or "originally to describe initial states and result or after for final states. What volume would a...
6. For a positive real number z, the difference 1.-z- is called the fractional part of r. Given arbitrary positive real numbers a and b, state a condition in terms of the fractional parts of and that is necessary and sufficient for la + bl = lal + Ibl Prove that this equation is true if and only if your condition holds. 7. Evaluate 10002+4 23k+5 k- 2 algebraically and simplify as much as possible. You ust show all steps....
Problem 5 answers:
3x coverage = 256.3114
30x coverage = 2563.1143
answer problem 6 pls
Problem 5 (1 point): Now let's think about sequencing reads and read length. How do could you determine how many reads you need from a given genome at a certain level of coverage? You can do this by multiplying the length of a genome by coverage divided by read length. As defined in a formula we have L(C/R) where L = genome length, c =...
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