Even Number Divisibility Problem The question is that for the equation $x = 25 + 5^k$ where $k$ is some random positive integer, can $x$ be divisible by $9$ for any $k$?
My first intuition is that since $25$ = odd and $5^k$=odd then $x$ must be an even number. Rule of divisibility by $9$ states that the sum of digits should be divisible by $9$.
Since $x$ is an even number :
The series :  $x = 18 , 36 , 54 , 72... $
Is there any $k$ value that corresponds to any number in this series? I tried to write a Python script and it seems like there are not any. What is the reason behind that?

You are correct that $25+5^k$ is divisible by $2$,
but that doesn't tell whether $25+5^k$ is divisible by $9$.
If you check $25+5^k$ for $k\in\{1,2,3,4,5,6\}$, you'll find that $25+5^\color{red}5$ is divisible by $9$.
$25+5^k$ grows much more quickly than $18k$.
