Given 2 as a primitive root of 29, construct a table of discrete logarithms, and use it to solve ...
Given 2 as a primitive root of 29, construct a table of discrete logarithms, and use it to solve the following congruences
b. x2− 4x − 16 ≡ 0(mod 29)
c. x7≡ 17(mod 29)
I need step by step calculations for b and c
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Given 2 as a primitive root of 29, construct a table of discrete logarithms, and use it to solve ...
G-2 is a primitive root modulo 19. Use the following table to assist you in the solution of the f...
g-2 is a primitive root modulo 19. Use the following table to assist you in the solution of the first two questions and 4(a). The most efficient solutions involve the use of the table and the application of theory; numerically correct solutions involving long computations will not receive full credit t1 2 3 4 567 89 10 11 12 13 14 151617 18 g 2 481613714918 17 15 11 36125101 Question 1. (a) Find the least positive residue of 126...
g 2 is a primitive root modulo 19. Use the following table to assist you in...
g 2 is a primitive root modulo 19. Use the following table to assist you in the solution of the first two questions and 4(a). The most efficient solutions involve the use of the table and the application of theory; numerically correct solutions involving long computations will not receive full credit t 1234567 8 9 10 11 12 13 14 15 16 1718 2 48 16 13 7 149 18 1715 11 3 6 12 5 10 1 (a) Find...
3. The number 2 is a primitive root modulo 19; the powers of 2 modulo 19...
3. The number 2 is a primitive root modulo 19; the powers of 2 modulo 19 are listed below 21 22232425 26 228221212213214215216217 21 2 48 16 13 7 14918 175 36 125 101 Use this table to solve r 7 mod 19.
4 [20 points] Given that 491 is a prime and 26 is primitive modulo 491, use the Pohlig- Hellman a...
4 [20 points] Given that 491 is a prime and 26 is primitive modulo 491, use the Pohlig- Hellman algorithm to solve 26 192 (mod 491). Be sure to show your work. You may need the following data. 2624 490 (mod 491) 26 101 (mod 491) 2610 414 (mod 491) 414 223 (mod 491) 4141 51 (mod 491) 1922451 (mod 491) 1928 381 (mod 491) 19210 3 (mod 491) 223 153 (mod 491)
4 [20 points] Given that 491 is...
Lidl US pietes une sidemem vers the question. Use common or natural logarithms to solve the...
Lidl US pietes une sidemem vers the question. Use common or natural logarithms to solve the exponential equation symbolically. 1 1) A) 1 In 27 + 2 3 In 3 B) = X = - In 3 In 27 + 18 In 3 C) X=- In 27 6 D) - In 27 3 In 3 - 2 Solve the logarithmic equation symbolically. 2) In x + In x4 = 5 A) x + x4 - 05 2) B) x =...
I need help with this question on Discrete Mathematics with Applications Thanks for your help! a....
I need help with this question
on Discrete Mathematics with Applications
Thanks for your help!
a. 8. Solve the following equivalences, if it cannot be solved, explain why not: 3x – 7 = 5(mod 7) b. 4x + 12 = 18(mod 24) C. 5x – 11 = 9(mod 13)
4. Use index calculus (and the tables on pages 213,216,217 in Apostol) to solve each of the follo...
4. Use index calculus (and the tables on pages 213,216,217 in Apostol) to solve each of the following congruences (a) 9r Ξ 7 (mod 17) (b) r511 (mod 19) (c) 5z Ξ 17 (mod 23) Table 10.1 g(p) is the smallest primitive root of the prime p 109 6 269 2439 15 617 3 3 3 2113 3271 6 443 2619 2821 2 5 2 127 3277 5 449 3631 3823 3 7 3 131 2281 3457 13 641 3827...
29. - 1 points SPRECALC7 4.4.034. Use the Laws of Logarithms to expand the expression DMyNotes...
29. - 1 points SPRECALC7 4.4.034. Use the Laws of Logarithms to expand the expression DMyNotes Need Help? Read It Talk te Tutor My Notes 30. 1/3 points || Previous Answers SPRECALC74.5.002. Let's solve the logarithmic equation log(3) + log(x - 2) -log(x). (a) First, we combine the logarithms on the LHS to get the equivalent equation log(x+1) X-10908). 1+2 X -X. (b) Next, we use the fact that log is one-to-one to get the equivalent equation (c) Now we...
Discrete structure For each of the following congruences if there is a solution, express the solution...
Discrete structure For each of the following congruences if there is a solution, express the solution in the form x ≡ some_number (mod some_modulus), e.g. x ≡ 6 (mod 9). To standardize answers, some_number should always be a value in the range {0, 1, 2, ..., some_modulus -1}. For example x ≡ 5 (mod 8) is OK but x ≡ 13 (mod 8) is not. If there is no solution say "No solution". You don't have to show work for any of the...
please help！！！ Discrete Structures For each of the following congruences if there is a solution, express...
please help！！！ Discrete Structures For each of the following congruences if there is a solution, express the solution in the form x ≡ some_number (mod some_modulus), e.g. x ≡ 6 (mod 9). To standardize answers, some_number should always be a value in the range {0, 1, 2, ..., some_modulus -1}. For example x ≡ 5 (mod 8) is OK but x ≡ 13 (mod 8) is not. If there is no solution say "No solution". You don't have to show work for any...
g-2 is a primitive root modulo 19. Use the following table to assist you in the solution of the first two questions and 4(a). The most efficient solutions involve the use of the table and the application of theory; numerically correct solutions involving long computations will not receive full credit t1 2 3 4 567 89 10 11 12 13 14 151617 18 g 2 481613714918 17 15 11 36125101 Question 1. (a) Find the least positive residue of 126...
g 2 is a primitive root modulo 19. Use the following table to assist you in the solution of the first two questions and 4(a). The most efficient solutions involve the use of the table and the application of theory; numerically correct solutions involving long computations will not receive full credit t 1234567 8 9 10 11 12 13 14 15 16 1718 2 48 16 13 7 149 18 1715 11 3 6 12 5 10 1 (a) Find...
3. The number 2 is a primitive root modulo 19; the powers of 2 modulo 19 are listed below 21 22232425 26 228221212213214215216217 21 2 48 16 13 7 14918 175 36 125 101 Use this table to solve r 7 mod 19.
4 [20 points] Given that 491 is a prime and 26 is primitive modulo 491, use the Pohlig- Hellman algorithm to solve 26 192 (mod 491). Be sure to show your work. You may need the following data. 2624 490 (mod 491) 26 101 (mod 491) 2610 414 (mod 491) 414 223 (mod 491) 4141 51 (mod 491) 1922451 (mod 491) 1928 381 (mod 491) 19210 3 (mod 491) 223 153 (mod 491)
4 [20 points] Given that 491 is...
Lidl US pietes une sidemem vers the question. Use common or natural logarithms to solve the exponential equation symbolically. 1 1) A) 1 In 27 + 2 3 In 3 B) = X = - In 3 In 27 + 18 In 3 C) X=- In 27 6 D) - In 27 3 In 3 - 2 Solve the logarithmic equation symbolically. 2) In x + In x4 = 5 A) x + x4 - 05 2) B) x =...
I need help with this question
on Discrete Mathematics with Applications
Thanks for your help!
a. 8. Solve the following equivalences, if it cannot be solved, explain why not: 3x – 7 = 5(mod 7) b. 4x + 12 = 18(mod 24) C. 5x – 11 = 9(mod 13)
4. Use index calculus (and the tables on pages 213,216,217 in Apostol) to solve each of the following congruences (a) 9r Ξ 7 (mod 17) (b) r511 (mod 19) (c) 5z Ξ 17 (mod 23) Table 10.1 g(p) is the smallest primitive root of the prime p 109 6 269 2439 15 617 3 3 3 2113 3271 6 443 2619 2821 2 5 2 127 3277 5 449 3631 3823 3 7 3 131 2281 3457 13 641 3827...
29. - 1 points SPRECALC7 4.4.034. Use the Laws of Logarithms to expand the expression DMyNotes Need Help? Read It Talk te Tutor My Notes 30. 1/3 points || Previous Answers SPRECALC74.5.002. Let's solve the logarithmic equation log(3) + log(x - 2) -log(x). (a) First, we combine the logarithms on the LHS to get the equivalent equation log(x+1) X-10908). 1+2 X -X. (b) Next, we use the fact that log is one-to-one to get the equivalent equation (c) Now we...
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