Question:
If $n$ is any natural number, then $6^{n}-5^{n}$ always ends with
(a) 1
(b) 3
(c) 5
(d) 7
[Hint: For any $n \in N, 6^{n}$ and $5^{n}$ end with 6 and 5 respectively. Therefore, $6^{n}-5^{n}$ always ends with $6-5=1$.]
Solution:
We know that $6^{n}$ will end in 6
And $5^{n}$ will end in 5 .
Now, $6^{n}-5^{n}$ always end with $6-5=1$
Hence the correct choice in (a).