Question

Working modulo 10.

Answer 1

What is the last digit of \(17^{17}\)?

I know that we have to do modulo \(10\), but this is the step I am confused about:\[17^{17}\equiv 7^{17} \pmod{10}\]

Answer 2

What is the property used in that step?

Answer 3

17 = 7 mod10
hence
17^n = 7^n mod10

Answer 4

Ah, ah. That clears everything up.

Answer 5

Thanks!

Answer 6

Glad in case I could help. ^_^