MathDB
Problems
Contests
International Contests
IMO Longlists
1992 IMO Longlists
30
30
Part of
1992 IMO Longlists
Problems
(1)
Find all m that P_m is divisible by 33^33
Source:
8/30/2010
Let
P
n
=
(
19
+
92
)
(
1
9
2
+
9
2
2
)
⋯
(
1
9
n
+
9
2
n
)
P_n = (19 + 92)(19^2 +92^2) \cdots(19^n +92^n)
P
n
=
(
19
+
92
)
(
1
9
2
+
9
2
2
)
⋯
(
1
9
n
+
9
2
n
)
for each positive integer
n
n
n
. Determine, with proof, the least positive integer
m
m
m
, if it exists, for which
P
m
P_m
P
m
is divisible by
3
3
33
.
33^{33}.
3
3
33
.
number theory
Divisibility
IMO Shortlist
IMO Longlist