MathDB

11.3

Part of 2023 Bulgarian Spring Mathematical Competition

Problems(1)

Positive integers representable as sum and difference of powers of 2

Source: Bulgarian Spring Tournament 2023 11.3

3/25/2023
A positive integer bb is called good if there exist positive integers 1=a1,a2,…,a2023=b1=a_1, a_2, \ldots, a_{2023}=b such that ∣ai+1−ai∣=2i|a_{i+1}-a_i|=2^i. Find the number of the good integers.
number theory