Can modular arithmetic help us find remainders and unit digits?

[donaldparida]

I am new to number theory and I heard from my friend that we can use modular arithmetic to conveniently find the unit digit of a number or the remainder obtained on dividing a number by another number such as the remainder obtained on dividing (x^y) by a. Is it possible?How can we do this?

 

[jedishrfu]

Are you looking for some method other than division?

The only one I know is Euclidean division:

https://en.wikipedia.org/wiki/Euclidean_division

mentioned in this article on modular arithmetic:

https://en.wikipedia.org/wiki/Modular_arithmetic