MathDB
Easy number theory in Taiwan TST

Source: 2021 Taiwan TST Round 3 Independent Study 1-N

May 1, 2021
number theoryming

Problem Statement

Let a1a_1, a2a_2, a3a_3, …\ldots be a sequence of positive integers such that a1=2021a_1=2021 and an+1−an=⌊an⌋.\sqrt{a_{n+1}-a_n}=\lfloor \sqrt{a_n} \rfloor. Show that there are infinitely many odd numbers and infinitely many even numbers in this sequence.
Proposed by Li4, Tsung-Chen Chen, and Ming Hsiao.
Back to ProblemsView on AoPS