f2001290 wrote:4. How many positive factors does N have?
1). N^2 has four positive factors.
2). 2N has three positive factors.

(1) If N^2 has three positive factors, then N is a prime; and if N^2 has four positive factors, then N doesn't exist as a positive integer, though N could be the square root of the product of two distinct primes, which is irrational, hence no positive factors for N are possible. No for zero in math, hence answered. Sufficient

(2) Now, this is bizarre! 2 N may have three positive factors only when N is 2, but this contradicts (1).

[spoiler]No answer to ambiguities any more...anybody?[/spoiler]