Question

Let $P\left(n\right)=5^n-2^n$. $P\left(n\right)$ is divisible by $3\lambda$ where $\lambda$ and $n$ both are odd positive integers, then the least value of $n$ and $\lambda$ will be

• A. $13$
• B. $11$
• C. $1$
• D. $5$

Answer 1

The correct option is C $1$

$5^n-2^n$ is divisible by $5-2=3$ always... Putting $n=\lambda =1$ which is the least odd positive integer, this works to be true.
Hence Option C