examday

Community mocks

Daniel J Smith Custom TMUA alpha · Q4

Number & counting

Let n>1n>1 be an integer. Consider the property P(n)P(n):

For all integers a,ba,b, if n∣abn\mid ab then n∣an\mid a or n∣bn\mid b.

Which of the following is correct?

AP(n)P(n) holds if and only if nn is prime
BP(n)P(n) holds if and only if nn is squarefree
CP(n)P(n) is sufficient but not necessary for nn to be prime
DP(n)P(n) holds if and only if nn is a prime power
EP(n)P(n) holds if and only if nn has at most two distinct prime factors

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.

Sign in to check your answerPractise the whole paper →