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a_1 is anything but 2

Source: Thailand TSTST 2024 P4

July 18, 2024
number theoryprime numbers

Problem Statement

The sequence (an)n∈N(a_n)_{n\in\mathbb{N}} is defined by a1=3a_1=3 and an=a1a2⋯an−1−1a_n=a_1a_2\cdots a_{n-1}-1 Show that there exist infinitely many prime number that divide at least one number in this sequences
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