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.
107 exam-style questions on Edexcel A Level Maths 1.1 Proof by Contradiction. Each one has a worked solution and a mark scheme showing where the marks go.