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calculator operations limited, if S > x^n + 1 then S > x^n + x - 1

Source: Tuymaada 2019 p4

July 22, 2019
Operationalgebracombinatoricsinequalities

Problem Statement

A calculator can square a number or add 11 to it. It cannot add 11 two times in a row. By several operations it transformed a number xx into a number S>xn+1S > x^n + 1 (x,n,Sx, n,S are positive integers). Prove that S>xn+xāˆ’1S > x^n + x - 1.
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