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Junior Balkan MO
1999 Junior Balkan MO
2
2
Part of
1999 Junior Balkan MO
Problems
(1)
Find the greatest comon divisor of the numbers A_1,..,A_1999
Source: JBMO 1999, Problem 2
10/30/2005
For each nonnegative integer
n
n
n
we define
A
n
=
2
3
n
+
3
6
n
+
2
+
5
6
n
+
2
A_n = 2^{3n}+3^{6n+2}+5^{6n+2}
A
n
=
2
3
n
+
3
6
n
+
2
+
5
6
n
+
2
. Find the greatest common divisor of the numbers
A
0
,
A
1
,
…
,
A
1999
A_0,A_1,\ldots, A_{1999}
A
0
,
A
1
,
…
,
A
1999
. Romania
modular arithmetic
number theory
greatest common divisor