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Contests
National and Regional Contests
Bulgaria Contests
Bulgaria JBMO Team Selection Test
2014 Bulgaria JBMO TST
8
8
Part of
2014 Bulgaria JBMO TST
Problems
(1)
Perfect square for all k
Source:
5/18/2015
Find the smallest positive integer
n
,
n,
n
,
such that
3
k
+
n
k
+
(
3
n
)
k
+
201
4
k
3^k+n^k+ (3n)^k+ 2014^k
3
k
+
n
k
+
(
3
n
)
k
+
201
4
k
is a perfect square for all natural numbers
k
,
k,
k
,
but not a perfect cube, for all natural numbers
k
.
k.
k
.
number theory