P1

Part of 2025 Israel TST

Problems(1)

Rational sequence reaches 1

Source: 2025 Israel TST Test 1 P1

A sequence starts at some rational number

x_1>1

, and is subsequently defined using the recurrence relation

x_{n+1}=\frac{x_n\cdot n}{\lfloor x_n\cdot n\rfloor }

k>0

x_k=1

number theoryalgebraSequence