Question

What is the last (units) digit of `17^1999+11^1999-7^1999` ?

Answer 1

`1`

Explanation:

Note that the unit place of `17^1999` will be the same as that of `7^1999` since the `10` in `17=10+7` will not affect the unit place. So when subtracted, `17^1999-7^1999` will have a `0` in the unit place.

So we are just concerned to find the unit place of `11^1999`, which is the same as `1^1999`, i.e. `1`.