1987 OIM Problems/Problem 4

Problem

We define the succession $p_n$ the following way: $p_1=2$ and for all $n$ more or equal than 2, $p_n$ is the greatest prime divisor of the expression: $p_1p_2p_1\cdots p_{n-1} +1$ Prove that $p_n$ is different than 5

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1987 OIM Problems/Problem 4

Problem

Solution