MathDB
Problems
Contests
International Contests
Balkan MO
1992 Balkan MO
1
1
Part of
1992 Balkan MO
Problems
(1)
Divisibility question
Source: Balkan MO 1992, Problem 1
4/25/2006
For all positive integers
m
,
n
m,n
m
,
n
define
f
(
m
,
n
)
=
m
3
4
n
+
6
−
m
3
4
n
+
4
−
m
5
+
m
3
f(m,n) = m^{3^{4n}+6} - m^{3^{4n}+4} - m^5 + m^3
f
(
m
,
n
)
=
m
3
4
n
+
6
−
m
3
4
n
+
4
−
m
5
+
m
3
. Find all numbers
n
n
n
with the property that
f
(
m
,
n
)
f(m, n)
f
(
m
,
n
)
is divisible by 1992 for every
m
m
m
. Bulgaria
number theory proposed
number theory