A cybersecurity firm uses a sequence of security tokens generated by the function f(n)=n2+n+17f(n) = n^2 + n + 17f(n)=n2+n+17, where n∈Nn \in \mathbb{N}n∈N. An analyst claims that every token produced by this function will be a prime number. Provide a counter-example to show that this claim is false.
A warehouse manager is attempting to organize P(n)=n2+2P(n) = n^2 + 2P(n)=n2+2 storage units into 4 equal zones. Use a proof by contradiction to show that, for all positive integers nnn, it is impossible to distribute the units such that each zone contains an equal integer number of units.
Practise AQA A Level Maths 1.4 A: Proof with exam-style questions for A Level Maths. 107 questions covering 1.4.1 Structure and methods of proof, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
