Hi, im quite new to the number theory topic, and i am self studying congruences right now.
some exercises are these, and im not quite sure how to solve them
1) find the remainder when 2^50 is divided by 7
2) fin the remainder when 41^65 is divided by 7
3) find the remainder when the sum (1^5)+(2^5)+(3^5)+....+(99^5)+(100^5) is divided by 7.
i know they might be easy, but im just looking for exercises by internet, and if someone can recomend me a good book for learning this, i will thank that.