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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