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B. 4651. A positive integer $\displaystyle n$ is said to be exotic if it is divisible by the number of its positive factors. Prove the following statements:

$\displaystyle a)$ If an exotic number is odd then it is a perfect square.

$\displaystyle b)$ There are infinitely many exotic numbers.

(3 points)

Deadline expired on 10 November 2014.

Statistics on problem B. 4651.
 264 students sent a solution. 3 points: 197 students. 2 points: 55 students. 1 point: 6 students. 0 point: 4 students. Unfair, not evaluated: 2 solutions.

• Problems in Mathematics of KöMaL, October 2014

•  Támogatóink: Morgan Stanley