MathDB

f(m) = f(m + 1), where f(n) is number of subsets of {1,...,n}

Source: 2023 NZMO - New Zealand Maths Olympiad Round 2 p4

September 2, 2023

combinatorics

Problem Statement

For any positive integer

n

, let

f(n)

be the number of subsets of

\{1, 2, . . . , n\}

whose sum is equal to

n

. Does there exist infinitely many positive integers

m

such that

f(m) = f(m + 1)

? (Note that each element in a subset must be distinct.)