MathDB

Positive integers representable as sum and difference of powers of 2

Source: Bulgarian Spring Tournament 2023 11.3

March 25, 2023

number theory

Problem Statement

A positive integer

b

is called good if there exist positive integers

1=a_1, a_2, \ldots, a_{2023}=b

such that

|a_{i+1}-a_i|=2^i

. Find the number of the good integers.