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Primes

Source: Indian RMO 2004 Problem 6

February 28, 2006

modular arithmeticnumber theoryrelatively prime

Problem Statement

Let

p_1, p_2, \ldots

be a sequence of primes such that

p_1 =2

and for

n\geq 1, p_{n+1}

is the largest prime factor of

p_1 p_2 \ldots p_n +1

. Prove that

p_n \not= 5

for any

n

.

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