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Number theory Difficulty 2.0 Junior Find the answer United Kingdom

For how many positive integer values of $n$ is $n^2 + 2n$ prime?

(A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) more than $3$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.