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Moldova Team Selection Test
2022 Moldova Team Selection Test
1
n^{5n-1}+n^{5n-2}+n^{5n-3}+n+1
n^{5n-1}+n^{5n-2}+n^{5n-3}+n+1
Source: Moldova TST 2022
April 1, 2022
number theory
Problem Statement
Show that for every integer
n
≥
2
n \geq 2
n
≥
2
the number
a
=
n
5
n
−
1
+
n
5
n
−
2
+
n
5
n
−
3
+
n
+
1
a=n^{5n-1}+n^{5n-2}+n^{5n-3}+n+1
a
=
n
5
n
−
1
+
n
5
n
−
2
+
n
5
n
−
3
+
n
+
1
is a composite number.
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