P6

Part of 2020/2021 Tournament of Towns

Problems(1)

Very beautiful NT

Source: 42nd International Tournament of Towns, Senior A-Level P6, Spring 2021

Find at least one real number

A{}

such that for any positive integer

n{}

the distance between

\lceil A^n\rceil

and the nearest square of an integer is equal to two.
Dmitry Krekov

number theoryFibonacciTournament of Towns