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Danube Competition in Mathematics
2016 Danube Mathematical Olympiad
4
Problem 4, Number Theory
Problem 4, Number Theory
Source: Danube Contest 2016, Romania
October 29, 2017
number theory
Problem Statement
4.Prove that there exist only finitely many positive integers n such that
(
n
1
+
1
)
(
n
2
+
2
)
.
.
.
(
n
n
+
n
)
(\frac{n}{1}+1)(\frac{n}{2}+2)...(\frac{n}{n}+n)
(
1
n
+
1
)
(
2
n
+
2
)
...
(
n
n
+
n
)
is an integer.
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