MathDB

9

Part of 1978 Romania Team Selection Test

Problems(1)

sequences for IMO preparation

Source: Romanian TST, Day 1, P9

9/28/2018
A sequence (xn)n≥0 \left( x_n\right)_{n\ge 0} of real numbers satisfies x0>1=xn+1(xn−⌊xn⌋), x_0>1=x_{n+1}\left( x_n-\left\lfloor x_n\right\rfloor\right) , for each n≥1. n\ge 1. Prove that if (xn)n≥0 \left( x_n\right)_{n\ge 0} is periodic, then x0 x_0 is a root of a quadratic equation. Study the converse.
quadraticsalgebraSequencesPeriodic sequence