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Take some time to read the following statements.

\([1]\) It is impossible to write \(1\) as the sum of the reciprocals of \(n\) odd integers when \(n\) is an even number.

\([2]\) If \(n\) is an integer greater than \(11\), then it is always possible to write \(n\) as the sum of two composite numbers.

\([3]\) If \(a\) is an irrational number, it is impossible for \(a^{\sqrt{2}}\) to be a rational number.

Which of these statements are correct?

Note: This problem is a part of the set "I Don't Have a Good Name For This Yet". See the rest of the problems here. And when I say I don't have a good name for this yet, I mean it. If you like problems like these and have a cool name for this set, feel free to comment here.


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