Question

find the orders of 1, 2, ..., 10(mod 11)

Answer #1

Find two values of integerx, such thatx≡1 (mod 5),x≡2 (mod 9)
andx≡ −1(mod 11).

**PLEASE SHOW ALL WORK***
1. Use Fernat's LT to find: 5^1314 (mod 11)
2. Find the gcd (729,135) using the Euclidean Algorithm
3. Find the Euler function for n=315.

(a) Solve
x ≡ 11 (mod 12), x ≡ 4 (mod 5), x ≡ 0 (mod 7)
(b) Find all the solutions of the following system:
x ≡ 5 (mod 6), x ≡ 4 (mod 11), x ≡ 3 (mod 17).

Find the smallest positive integer x such that: x mod 2=1 x mod
3=2 and x mod 5=3
What is the next integer with this property?

solve the following set of simultaneous congruence x=1
mod (2) x= 2 mod(3) x =3:mod (5) x= 4 mod (11)

Find all solutions to each congruence.
(a) 2x − 3 ≡ 2 (mod 7)
(b) 3x + 4 ≡ 1 (mod 5)
(c) 3x ≡ 6 (mod 9)
(d) 14x ≡ 11 (mod 15)

Fill in the blanks and Make sure your answer is reduced.
Find inverse of 2 (mod 17).
2^-1 ≡ ____________(mod 17).
Find inverse of 34 (mod 89).
34^-1 ≡ _____________(mod 89).
Find inverse of 144 (mod 233).
144^-1 ≡ ___________(mod 233).
Find inverse of 200 (mod 1001).
200^-1 ≡ ___________ (mod 1001).
Fill in the blanks and If x has no solution, write "NA" on all
the answer blanks.
Find all x such that 34x ≡ 77 (mod 89).
x...

solve the system of the congruences using Chinese Remainder.
x≡2 (mod 11)
x≡8 (mod 13)
x≡5 (mod 16)

Find all the solutions of 3x2 + 2x – 2 = 1 (mod
29).

find an integer x such that 3x=2 mod 5, and 4x=5 mod 7

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