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1988 All Soviet Union Mathematical Olympiad
471
ASU 471 All Soviet Union MO 1988 (1 + 1/n)^{n+1} = (1 + 1/1998)^{1998}
ASU 471 All Soviet Union MO 1988 (1 + 1/n)^{n+1} = (1 + 1/1998)^{1998}
Source:
August 7, 2019
diophantine
Diophantine equation
exponential
algebra
number theory
Problem Statement
Find all positive integers
n
n
n
satisfying
(
1
+
1
n
)
n
+
1
=
(
1
+
1
1998
)
1998
\left(1 +\frac{1}{n}\right)^{n+1} = \left(1 + \frac{1}{1998}\right)^{1998}
(
1
+
n
1
)
n
+
1
=
(
1
+
1998
1
)
1998
.
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