MathDB

Denote by

\lceil x \rceil

the greatest integer less than or equal to

x

and by

S(x)

the sequence

\lceil x \rceil, \lceil 2x \rceil, \lceil 3x \rceil, \dots.

Prove that there are distinct real solutions

\alpha

and

\beta

of the equation

x^3-10x^2+29x-25=0

such that infinitely many positive integers appear both in

S(\alpha)

and in

S(\beta).

Problem Statement