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Found problems: 26

2019 Tuymaada Olympiad, 4
Tags: operation , algebra , combinatorics , inequalities
A calculator can square a number or add $1$ to it. It cannot add $1$ two times in a row. By several operations it transformed a number $x$ into a number $S > x^n + 1$ ($x, n,S$ are positive integers). Prove that $S > x^n + x - 1$.