## ParthKohli Group Title Working modulo 10. one year ago one year ago

1. ParthKohli Group Title

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:$17^{17}\equiv 7^{17} \pmod{10}$

2. ParthKohli Group Title

What is the property used in that step?

3. shubhamsrg Group Title

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

4. ParthKohli Group Title

Ah, ah. That clears everything up.

5. ParthKohli Group Title

Thanks!

6. shubhamsrg Group Title

Glad in case I could help. ^_^