MathDB

Let

k

be a positive integer. A natural number

m

is called

k

-typical if each divisor of

m

leaves the remainder

1

when being divided by

k

. Prove: a) If the number of all divisors of a positive integer

n

(including the divisors

1

and

n

) is

k

-typical, then

n

is the

k

-th power of an integer. b) If

k > 2

, then the converse of the assertion a) is not true.

Problem Statement