MathDB

10.1

Part of 2000 Saint Petersburg Mathematical Olympiad

Problems(1)

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

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

4/22/2023
Sequences x1,x2,…,x_1,x_2,\dots, and y1,y2,…,y_1,y_2,\dots, are defined with x1=18x_1=\dfrac{1}{8}, y1=110y_1=\dfrac{1}{10} and xn+1=xn+xn2x_{n+1}=x_n+x_n^2, yn+1=yn+yn2y_{n+1}=y_n+y_n^2. Prove that xm≠ynx_m\neq y_n for all m,n∈Z+m,n\in\mathbb{Z}^{+}.
[I]Proposed by A. Golovanov
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