School of Mathematics and Statistics

MATH2400 FINITE MATHEMATICS

Trimester 2, 2021                                        TEST 2 (SAMPLE)                                        VERSION 4

● Time Allowed: 30 minutes + 15 minutes for scanning and uploading

● Total Number of Marks: 30

● For each question you must show your working; unsubstantiated answers will not gain positive marks

● Submit each question separately, clearly marking the files Q1, Q2, Q3

1. [10 marks]

i) Solve the simultaneous system of an equation and a congruence

ii) Solve the simultaneous congruences

2. [10 marks]

i) Someone announces the intention to use twin primes, that is, primes p and q with q = p + 2 to create a modulus M = pq for the RSA encryption. Show that this is very insecure.

ii) Is this true that if for some integers a and p with gcd(a, p) = 1 we have

then p is prime?

3. [10 marks]

Consider the code which encodes

i) What is the information rate of this code?

ii) Can this code detect two errors?

END OF TEST