Week 3

Question 1

State and apply the Chinese Remainder Theorem

Question 2

Define 𝜑(𝑛)

Question 3

Calculate 𝜑(𝑛) when the prime factorisation of 𝑛 is known

Question 4

Appreciate that 𝜑(𝑛) is multiplicative

Question 5

Define the number theoretic functions 𝑢(𝑛), 𝑁(𝑛), 𝜎(𝑛) and 𝜏(𝑛)

Question 6

Compute 𝑢(𝑛), 𝑁(𝑛), 𝜎(𝑛) and 𝜏(𝑛) when the prime factorisation of 𝑛 is known

Question 7

State the definition of a multiplicative function

Question 8

Prove that if a number theoretic function 𝑔 is multiplicative then ∑_𝑑∣𝑛𝑔(𝑑) is also multiplicative

Question 9

Appreciate that 𝑢(𝑛), 𝑁(𝑛), 𝜎(𝑛) and 𝜏(𝑛) are all multiplicative