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 $1$

$P\left(n\right)=5^n-2^n$
Let $\lambda =1$, we get $P\left(1\right)=5^1-2^1=3$
Similarly for,$n=5,P\left(5\right)=5^5-2^5=3125-32=3093=3\times 1031$
In this case $\lambda =1031$
Similarly we can check the result for other cases and find that the least value of $\lambda$ and n is $1$.
Ans: C