MathDB
Rational sequence reaches 1

Source: 2025 Israel TST Test 1 P1

October 28, 2024
number theoryalgebraSequence

Problem Statement

A sequence starts at some rational number x1>1x_1>1, and is subsequently defined using the recurrence relation xn+1=xn⋅n⌊xn⋅n⌋x_{n+1}=\frac{x_n\cdot n}{\lfloor x_n\cdot n\rfloor } Show that k>0k>0 exists with xk=1x_k=1.
Back to ProblemsView on AoPS