MathDB
Problems
Contests
National and Regional Contests
Greece Contests
Greece National Olympiad
2022 Greece National Olympiad
2
2
Part of
2022 Greece National Olympiad
Problems
(1)
Number Theory involving divisors
Source: Greece National Olympiad 2022, Problem 2
2/26/2022
Let
n
>
4
n>4
n
>
4
be a positive integer, which is divisible by
4
4
4
. We denote by
A
n
A_n
A
n
the sum of the odd positive divisors of
n
n
n
. We also denote
B
n
B_n
B
n
the sum of the even positive divisors of
n
n
n
, excluding the number
n
n
n
itself. Find the least possible value of the expression
f
(
n
)
=
B
n
−
2
A
n
,
f(n)=B_n-2A_n,
f
(
n
)
=
B
n
−
2
A
n
,
for all possible values of
n
n
n
, as well as for which positive integers
n
n
n
this minimum value is attained.
number theory
Divisors