China TST 2002

For discussing Olympiad Level Number Theory problems
tanmoy
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Joined: Fri Oct 18, 2013 11:56 pm
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China TST 2002

Unread post by tanmoy » Wed Oct 19, 2016 10:41 pm

Let $p_{i} \geq 2,i=1,2, \cdots n$ be $n$ integers such that any two of them are relatively prime. Let:

\[P=\{ x=\sum_{i=1}^{n} x_{i} \prod_{j=1, j \neq i}^{n} p_j \mid x_i \text{is a non-negative integer},i=1,2,\cdots n\}\]
Prove that the biggest integer $ M$ such that $M \not\in P$ is greater than $\dfrac {n-2} {2} \cdot \prod_{i =1}^{n} p_i$,and also find $M$
"Questions we can't answer are far better than answers we can't question"

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