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Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2002 Junior Balkan Team Selection Tests - Moldova
1
1
Part of
2002 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
a = n^5 + 6n^3 + 8n ¸ b = n^4 + 4n^2 + 3 are relative prime of have gcd 3
Source: 2002 Moldova JBMO TST p1
2/25/2021
For any integer
n
n
n
we define the numbers
a
=
n
5
+
6
n
3
+
8
n
a = n^5 + 6n^3 + 8n
a
=
n
5
+
6
n
3
+
8
n
¸
b
=
n
4
+
4
n
2
+
3
b = n^4 + 4n^2 + 3
b
=
n
4
+
4
n
2
+
3
. Prove that the numbers
a
a
a
and
b
b
b
are relatively prime or have the greatest common factor of
3
3
3
.
number theory
greatest common divisor