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.
