If the integer n is greater than 1, is n equal to 2?

(2) The difference of any two distinct positive factors of n is odd

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I guess the statement (1) is a trap. We don't need statement (1). Statement (2) alone is sufficient.

(2) 2 is the only number which satisfies the condition stated in the statement (2).

All the odd numbers has at least two odd positive factors (1 and itself), and thus the difference of these two factors is even.

All the even numbers except 2 has at least two even positive factors (2 and itself) and thus the difference of these two factors is even.

Therefore, 2 is the only number which satisfies the statement (2).

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