MathDB

Given a positive integer

n \ge 2

, we define

f(n)

to be the sum of all remainders obtained by dividing

n

by all positive integers less than

n

. For example dividing

5

with

1, 2, 3

and

4

we have remainders equal to

0, 1, 2

and

1

respectively. Therefore

f(5) = 0 + 1 + 2 + 1 = 4

. Find all positive integers

n \ge 3

such that

f(n) = f(n - 1) + (n - 2)

Problem Statement