CMI entrance 19#2
Source:
October 31, 2019
complex numbersDiophantine equationCMIalgebra
Problem Statement
Count the number of roots of of the equation over complex numbers that satisfy
\begin{align*}
\vert \omega + 1 \vert \geq \sqrt{2 + \sqrt{2}}
\end{align*}
Find all real numbers that satisfy following equation
\begin{align*}
\frac{ 8^x + 27^x }{ 12^x + 18^x } = \frac{7}{6}
\end{align*}