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set of primes less than $10000$

Source: 8-th Taiwanese Mathematical Olympiad 1999

January 20, 2007

number theory unsolvednumber theory

Problem Statement

Let

P^{*}

be the set of primes less than

10000

. Find all possible primes

p\in P^{*}

such that for each subset

S=\{p_{1},p_{2},...,p_{k}\}

of

P^{*}

with

k\geq 2

and each

p\not\in S

, there is a

q\in P^{*}-S

such that

q+1

divides

(p_{1}+1)(p_{2}+1)...(p_{k}+1)

.

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