MathDB

For a positive integer

n>2

, consider the

n-1

fractions

\dfrac21, \dfrac32, \cdots, \dfrac{n}{n-1}

The product of these fractions equals

n

, but if you reciprocate (i.e. turn upside down) some of the fractions, the product will change. Can you make the product equal 1? Find all values of

n

for which this is possible and prove that you have found them all.

Problem Statement