Question

If $n$ is any natural numbers, then $6^n-5^n$ always ends with_________

Answer 1

$6^n-5^n$

For $n=1$

$6^1-5^1=6-5=01$

$\Rightarrow$ Unit digit is $1$, i.e., ends with $1$.

For $n=2$

$6^2-5^2=36-25=1$

$\Rightarrow$ Unit digit is $1$, i.e., ends with $1$.

For $n=3$

$6^3-5^3=216-125=91$

$\Rightarrow$ Unit digit is $1$, i.e., ends with $1$.

By continuity, we can say that $(6^n-5^n)$ always ends with $1$.