MathDB

Prove that $x_m\neq y_n$ for all $m$ and $n$.

Source: St. Petersburg MO 2000, 10th grade, P1

April 22, 2023

algebrasequances

Problem Statement

Sequences

x_1,x_2,\dots,

and

y_1,y_2,\dots,

are defined with

x_1=\dfrac{1}{8}

,

y_1=\dfrac{1}{10}

and

x_{n+1}=x_n+x_n^2

,

y_{n+1}=y_n+y_n^2

. Prove that

x_m\neq y_n

for all

m,n\in\mathbb{Z}^{+}

.
[I]Proposed by A. Golovanov

Back to Problems View on AoPS