MathDB

A5

Part of 2015 Balkan MO Shortlist

Problems(1)

if (a^{m+1}-1)/(a^m-1)=(b^{n+1}-1)/(b^n-1)=c then a^m c^n > b^n c^{m}

Source: Balkan BMO Shortlist 2015 A5

8/5/2019
Let m,nm, n be positive integers and a,ba, b positive real numbers different from 11 such thath m>nm > n and am+1−1am−1=bn+1−1bn−1=c\frac{a^{m+1}-1}{a^m-1} = \frac{b^{n+1}-1}{b^n-1} = c. Prove that amcn>bncma^m c^n > b^n c^{m}
(Turkey)
inequalitiesalgebraExponential inequalityexponentialExponential equation