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All-Soviet-Union Mathematical Olympiad

Algebra Difficulty 4.7 AIME Prove it Soviet Union

Problem:

Find all positive integers nn satisfying (1+1/n)n+1=(1+1/1998)1998.(1 + 1 / n)^{n + 1} = (1 + 1 / 1998)^{1998}.

Solution

Solution:

Answer: no solutions.

We have (1+1/n)n+1>e>(1+1/n)n.(1 + 1 / n)^{n + 1} > e > (1 + 1 / n)^{n}.

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