MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2021 Latvia Baltic Way TST
P15
P15
Part of
2021 Latvia Baltic Way TST
Problems
(1)
Most trivial TST NT ever seen
Source: Latvia BW TST 2021 P15
9/26/2021
Denote by
s
(
n
)
s(n)
s
(
n
)
the sum of all natural divisors of
n
n
n
which are smaller than
n
n
n
. Does there exist a positive integer
a
a
a
such that the equation
s
(
n
)
=
a
+
n
s(n)=a+n
s
(
n
)
=
a
+
n
has infinitely many solutions in positive integers?
number theory
trivial