1987 OIM Problems/Problem 4

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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

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe2.htm