1. Use backward substitution to solve: x=8 (mod 11) x=3 (mod 19)

1. Use backward substitution to solve:

x=8 (mod 11)

x=3 (mod 19)

2. Fine the subgroup of Z24 (the operation is addition) generates by the element 20.

3. Find the order of the element 5 in (z/7z)

Expert Solution

Colby Messinger answered 2 years ago

Use the Extended Euclid's Algorithm to solve ƒ-1 for 8 mod 11

1. Use the Extended Euclid's Algorithm to solve ƒ-1 for 8 mod 11 2. Use the...

1. Use the Extended Euclid's Algorithm to solve ƒ-1 for 8 mod 11 2. Use the max function to calculate max3(x, y, z) if x = 2, y = 6, z = 5. Show your work!

Using the Chinese remainder theorem solve for x: x = 1 mod 3 x = 5...

Using the Chinese remainder theorem solve for x: x = 1 mod 3 x = 5 mod 7 x = 5 mod 20 Please show the details, I`m trying to understand how to solve this problem since similar questions will be on my exam.

1. use back substitution to solve for x and y in the following equation: 417x +...

1. use back substitution to solve for x and y in the following equation: 417x + 362y = 1 2. Use contradiction to show that there is no integer that is both even and odd 3. For all integers a, b, c, and d, if a/c and b/d then ab/cd 4. For all integrrs a, b, and c, if a/b and b/c then ab/c

Solve the following system of congruences: x ≡ 2 (mod 14) x ≡ 16 (mod 21)...

Solve the following system of congruences: x ≡ 2 (mod 14) x ≡ 16 (mod 21) x ≡ 10 (mod 30)

a. Solve 7x + 5 ≡ 3 (mod 19). b. State and prove the Chinese Remainder Theorem

a. Solve 7x + 5 ≡ 3 (mod 19). b. State and prove the Chinese Remainder Theorem c. State and prove Euler’s Theorem. d. What are the last three digits of 9^1203? e. Identify all of the primitive roots of 19. f. Explain what a Feistel system is and explain how to decrypt something encoded with a Feistel system. Prove your result.

Use the Pohlig-Hellman algorithm to solve 19x ≡ 184 (mod 337) for x. Write out at...

Use the Pohlig-Hellman algorithm to solve 19x ≡ 184 (mod 337) for x. Write out at least one successive squaring in detail, and at least one instance of the Chinese Remainder Theorem.

a) Use Fermat’s little theorem to compute 52003 mod 7, 52003 mod 11, and 52003 mod 13.

a) Use Fermat’s little theorem to compute 52003 mod 7,52003 mod 11, and 52003 mod 13. b) Use your results from part (a) and the Chinese remaindertheorem to find 52003 mod 1001. (Note that1001 = 7 ⋅ 11 ⋅ 13.)

Use the following distribution of sample data X=study hours 12 12 11 8 8 3 and...

Use the following distribution of sample data X=study hours 12 12 11 8 8 3 and calculate the mean, SS, the variance and the standard deviation. Mean=? SS=? variance=? standard deviation=? The above data (in question #2)represents data collected from a small random sample of students who reported how many hours they study per week. Use the mean, standard deviation and n from the data above and alpha =.05 in a hypothesis test to determine whether students spend the recommended 12...

Compute the following: (a) 13^2018 (mod 12) (b) 8^11111 (mod 9) (c) 7^256 (mod 11) (d)...

Compute the following: (a) 13^2018 (mod 12) (b) 8^11111 (mod 9) (c) 7^256 (mod 11) (d) 3^160 (mod 23)

Question