MathDB

P6

Part of 2021 Peru Cono Sur TST.

Problems(1)

Prove that there are no such 2021 numbers

Source: 2021 Peru Cono Sur TST P6

7/11/2023
Prove that there are no positive integers a1,a2,…,a2021a_1, a_2, \ldots , a_{2021} (not necessarily distinct) such that for k=1,2,3,…,2021k = 1, 2, 3, \ldots , 2021 the number of elements in the set Ak={j∈N:1≤j≤2021 and aj∣k}A_k = \{ j \in \mathbb{N} : 1 \le j \le 2021 \text{ and } a_j|k \} be exactly aka_k.
number theory