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Let

k>1

be a positive integer and

n>2018

an odd positive integer. The non-zero rational numbers

x_1,x_2,\ldots,x_n

are not all equal and:

x_1+\frac{k}{x_2}=x_2+\frac{k}{x_3}=x_3+\frac{k}{x_4}=\ldots=x_{n-1}+\frac{k}{x_n}=x_n+\frac{k}{x_1}

Find the minimum value of

k

, such that the above relations hold.

Problem Statement