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Iberoamerican 1987.5

Source: IberoAmerican 1987 Q4

October 27, 2006
number theoryalgebra proposedalgebra

Problem Statement

The sequence (pn)(p_n) is defined as follows: p1=2p_1=2 and for all nn greater than or equal to 22, pnp_n is the largest prime divisor of the expression p1p2p3…pn−1+1p_1p_2p_3\ldots p_{n-1}+1. Prove that every pnp_n is different from 55.
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