1. Find all solutions to the following linear congruences using Fermat’s Little Theorem or Euler’s Theorem...

1. Find all solutions to the following linear congruences using Fermat’s Little Theorem or Euler’s Theorem to help you. Show all your steps.

(a) 3462x ≡ 6 173 (mod 59)

(b) 27145x ≡ 1 (mod 42)

Expert Solution

Colby Messinger answered 2 years ago

1. Find the multiplicative inverse of 14 in GF(31) domain using Fermat’s little theorem. Show your...

1. Find the multiplicative inverse of 14 in GF(31) domain using Fermat’s little theorem. Show your work. 2 Using Euler’s theorem to find the following exponential: 4200 mod 27. Show how you have employed Euler’s theorem here.

Q4. Find the multiplicative inverse of 14 in GF(31) domain using Fermat’s little theorem. Show your...

Q4. Find the multiplicative inverse of 14 in GF(31) domain using Fermat’s little theorem. Show your work Q5. Using Euler’s theorem to find the following exponential: 4200mod 27. Show how you have employed Euler’s theorem here

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.)

NUMBER THEORY 1.Find all the possible solutions for the following diphantine equations by using the euclidian...

*NUMBER THEORY* 1.Find all the possible solutions for the following diphantine equations by using the euclidian algorithim. You must show all the process to get credit. a. 3x + 5y = 7 b. 3x − 12y = 7 c. 1990x − 173y = 11 d. 21x + 48y = 6 e. 2x + 3y + 5z = 11

2. (a) Solve the complex equation (1+?)?3−[1+??(?3)]=0 and list all possible solutions in Euler’s form with...

2. (a) Solve the complex equation (1+?)?3−[1+??(?3)]=0 and list all possible solutions in Euler’s form with principal arguments. (b) Express the complex number ?=(1−sin?+?cos?)20 in Euler’s form.

Using Fermat't Little Theorem for primality test. Answer the following. Show work for credit. (a) Test...

Using Fermat't Little Theorem for primality test. Answer the following. Show work for credit. (a) Test whether each of the following numbers is primes: 101, 341, and 1105. Try at least two bases if needed, and state if the number is pseudoprime to any base you try. You may use a claculator to compute large powers. (MS Excel can be used) (b) Find a composit number that is pseudoprime to base 3 and 7 but not pseudoprime to base 2...

6. Euler’s theorem (one of many): A function ?(?1,?2,…,??) is said to be homogeneous of degree...

6. Euler’s theorem (one of many): A function ?(?1,?2,…,??) is said to be homogeneous of degree k, if for any ? > 0, ?(??1,??2,…,???) ≡ ?^? ?(?1,?2,…,??) a. Explain why a demand function ?(??,??,?) is homogeneous of degree 0. b. Using part a), prove the sum of the income elasticity and the cross-price elasticity equals the price elasticity of demand. Hint: differentiate the demand function identity in part a) with respect to λ.

Find all solutions to the following equations: (a) √2x − 2 = √x + 1 (b)...

Find all solutions to the following equations: (a) √2x − 2 = √x + 1 (b) x4 − 5x2 + 6 = 0 (c) |3x − 7| < 5 (d) |ax + b| ≥ c Explain step by step please Suppose 4 is a right triangle with leg-lengths a and b and hypotenuse c. Find the missing side: (a) a = 3, b = 4, c =? (b) a = 12, c = 13, b =? (c) a = 6,...

Predict the form of the solution (study limits) and find all of the solutions using the...

Predict the form of the solution (study limits) and find all of the solutions using the Frobenius method approach. Write indicial equation, find its roots, the recurrence relation, and the first four terms terms of each series solution for xy"+y'+x^2y=0

find solutions to the following using Excel's matrix operations?

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