Problem B. 4651. (October 2014)

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 pont)

Deadline expired on November 10, 2014.

Statistics:

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 solutionss.

Problems in Mathematics of KöMaL, October 2014