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Take some time to read the following statements.

[1][1] It is impossible to write 11 as the sum of the reciprocals of nn odd integers when nn is an even number.

[2][2] If nn is an integer greater than 1111, then it is always possible to write nn as the sum of two composite numbers.

[3][3] If aa is an irrational number, it is impossible for a2a^{\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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