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.
368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.