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Problems
Contests
International Contests
Pan African
2016 PAMO
3
PAMO 2016 Q3
PAMO 2016 Q3
Source: PAMO 2016
April 29, 2016
number theory
Integer Polynomial
greatest common divisor
Problem Statement
For any positive integer
n
n
n
, we define the integer
P
(
n
)
P(n)
P
(
n
)
by :
P
(
n
)
=
n
(
n
+
1
)
(
2
n
+
1
)
(
3
n
+
1
)
.
.
.
(
16
n
+
1
)
P(n)=n(n+1)(2n+1)(3n+1)...(16n+1)
P
(
n
)
=
n
(
n
+
1
)
(
2
n
+
1
)
(
3
n
+
1
)
...
(
16
n
+
1
)
.Find the greatest common divisor of the integers
P
(
1
)
P(1)
P
(
1
)
,
P
(
2
)
P(2)
P
(
2
)
,
P
(
3
)
,
.
.
.
,
P
(
2016
)
P(3),...,P(2016)
P
(
3
)
,
...
,
P
(
2016
)
.
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