MathDB

4

Part of 1999 Taiwan National Olympiad

Problems(1)

set of primes less than $10000$

Source: 8-th Taiwanese Mathematical Olympiad 1999

1/20/2007
Let P∗P^{*} be the set of primes less than 1000010000. Find all possible primes p∈P∗p\in P^{*} such that for each subset S={p1,p2,...,pk}S=\{p_{1},p_{2},...,p_{k}\} of P∗P^{*} with k≥2k\geq 2 and each p∉Sp\not\in S, there is a q∈P∗−Sq\in P^{*}-S such that q+1q+1 divides (p1+1)(p2+1)...(pk+1)(p_{1}+1)(p_{2}+1)...(p_{k}+1).
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