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MathNet 2016-part-06 — 184 problems (EN–VI) Question 177

Math Olympiad Vault · MathNet 2016-part-06 — 184 problems (EN–VI)

Question 177

Petryk programmed calculator in such a way that if there is number $x$ on the screen and then the button «$\Rightarrow$» is pressed, number $\frac{x-1}{x+1}$ appears on the screen. Petryk pressed the button «$\Rightarrow$» 2014 times, and then 2016 appeared on the screen. What number was on the screen at the beginning? The screen can show not only integer numbers.