MathDB

Let

0<c<1

be a given real number. Determine the least constant

K

such that the following holds: For all positive real

M

that is greater than

1

, there exists a strictly increasing sequence

x_0, x_1, \ldots, x_n

(of arbitrary length) such that

x_0=1, x_n\geq M

and

\sum_{i=0}^{n-1}\frac{\left(x_{i+1}-x_i\right)^c}{x_i^{c+1}}\leq K.

(From 2020 IMOCSL A5. I think this problem is particularly beautiful so I want to make a separate thread for it :D )

Problem Statement