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French Mathematical Olympiad
1999 French Mathematical Olympiad
Problem 2
diophantine, exponential sum
diophantine, exponential sum
Source: 1999 France MO P2
April 10, 2021
number theory
Diophantine equation
Problem Statement
Find all natural numbers
n
n
n
such that
(
n
+
3
)
n
=
∑
k
=
3
n
+
2
k
n
.
(n+3)^n=\sum_{k=3}^{n+2}k^n.
(
n
+
3
)
n
=
k
=
3
∑
n
+
2
k
n
.
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