Exam-Style Question on Number
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 182. This question is similar to one that appeared on a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.
This expression can be used to generate a sequence of numbers.$$n^2+n + 5$$
(a) Work out the first three terms of this sequence.
(b) What is the smallest value of \(n\) that produces a term of the sequence that is not a prime number?
(c) Is it true that odd square numbers have exactly three factors? Explain and justify your answer.
(d) Seymour is thinking of a number.
Find the two possible numbers that Seymour could be thinking of.
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Here is a related challenge called the Prison Cell Problem.
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