MathDB

Integers that cannot be represented in a certain manner

Source: Kvant Magazine No. 2 2020 M2592

March 10, 2023

number theorypolynomialKvant

Problem Statement

Let

P(x)

be a polynomial taking integer values at integer inputs. Are there infinitely many natural numbers that are not representable in the form

P(k)-2^n

where

n{}

and

k{}

are non-negative integers?
Proposed by F. Petrov