Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# 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