MathDB

3

Part of 2024 Mathematical Talent Reward Programme

Problems(2)

MTRP OBJECTIVE Q3

Source: MTRP 2024

3/16/2024
The smallest positive integer which can be expressed as sum of positive perfect cubes (possibly with repetition and/or with a single element sum) in at least two different ways in (A)8(A) 8 (B)1729(B) 1729 (C)2023(C) 2023 (D)2024(D) 2024
number theory
MTRP SUBJECTIVE Q3

Source: MTRP 2024

3/16/2024
P(n)\mathcal{P}(\mathbb{n}) denotes the collection of all subsets of N\mathbb{N}. Let f:N⟶P(n)f:\mathbb{N} \longrightarrow \mathcal{P}(\mathbb{n}) be a function such that f(n)=⋃d∣n,d<n,n≥2f(d)f(n) = \bigcup_{d|n,d<n,n \geq 2} f(d) Find the number of such functions ff for which the range of f⊆f \subseteq {1,2,3....20241,2,3....2024}.
number theory