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)
Compute additive and multiplicative inverses of 7 and 9 in Z11
(mod 11).
Find out whether or not 4 and 7 have multiplicative inverse in
Z14 (mod 14).
Let S be the set of even integers under the operations of
addition and multiplication. Is S a ring? Is it commutative? Is it
a field? Justify your answer.
Compute the multiplicative inverse of 9 under modulo 31 using
the extended Euclid’s algorithm.
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 work
Q5. Using Euler’s theorem to find the following exponential:
4200mod 27. Show how you have employed Euler’s theorem here
Use the Chinese remainder theorem. Say that:
x = 6 mod 10
x = 4 mod 9
x = 2 mod 7
Find what is x modulo 10 · 9 ·
7.
Please show all work and the correctness of your analysis.