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SMO 2009 Junior Round 1 Question 19

SMO · SMO 2009 Junior Round 1

Question 19

Let $p,q$ be two consecutive prime numbers. For some fixed integer $n$, the set $\{n-1,3n-19,38-5n,7n-45\}$ represents $\{p,2p,q,2q\}$, not necessarily in that order. Find $n$.