Georgetown University Modular Arithmetic Questions

Description

1. Consider the equation

197x?367 mod 419

Suppose that I claimed that x?155 is the solution. Write a few lines (line?) of Python code which verify that I am correct.

2. Do the same with the claim that x?25 is a solution of the equation

x2 ?4x+ 19 ?125 mod 419

3. Solve the following modular equations.

(a) 7x?6 mod 25

(b) 3x+ 2 ?1 ?xmod 21

(c) 10001x?4 mod 101

Hint: What is 100 mod 101? What is 10000 mod 101?

(d) 50x?x?2 mod 155

4. Find an integer n>2 where 3 does not divide n and 3n?1 ? 1 mod n

5. Compute the following number without the use of a computer:

11371495005541085992897640328743727364597182772002 mod 101

Your answer should be among 0,1,2,…,100. Note that 101 is a prime number.

6. Find a prime number p for which the equation

x2 ??1 mod p

has no solution.

7. Find a prime number p for which the equation

x2 ??1 mod p

has a solution.

8. Compute the following numbers, where ?is Euler’s totient function.

(a) ?(2)

(b) ?(15)

(c) ?(27)

(d) ?(21000)

9. Compute

52^999 mod 21000

10. Find a generator mod 191 (which is a prime number).

Get your college paper done by experts

Do my question How much will it cost?

Place an order in 3 easy steps. Takes less than 5 mins.

0 replies

Leave a Reply

Want to join the discussion?
Feel free to contribute!

Leave a Reply

Your email address will not be published. Required fields are marked *