What is 50³⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰³ (mod 221) ?
Computer did tell me the result firsthand, but tearing it down it would be:
221 = 13*17, LCM( 13-1 , 17-1 ) = 48
300000000003 = 3 (mod 48)
50³=135 (mod 221)
50³⁰⁰⁰⁰⁰⁰⁰⁰⁰⁰³ = 135 (mod 221)
amirite?
Which exponent did i use to find 55ˣ=217 (mod 221)?
55¹¹=217 (mod 221)
I just bruteforced this one ( ͡° ͜ʖ ͡°)
Exactly correct. I was nice in the second one choosing a small exponent so people can find it without to much effort.
how did your computer tell you, what did you use?
$ python
>>> pow(50,300000000003,221)
135
I also used a python script to find the second value.
I did try a few online resources and they were unable to compute it. Good to now that basic python knows how to simplify these calculations.