576^1289 = x (mod 11745)

0<x>1745


Why is it so hard finding that x
Could anyone explain how you find this? I clearly need a bigger calculator to calculate this lol

This post was edited by twiiztedacer on Mar 5 2014 03:00pm

its unsolvable

From what I understand you don't even need that high of a number. There is a mod function theorem that you should have learned before receiving this.

yeah, you are suppose to make the number smaller but I've forgotten how to do it :'(

576^1289 % 11745 = 11016
so
(576^1289 - x) % 11745 = 0
won't be happening until x = 11016, which is outside your domain.

I smell a typo on that domain, it should be 0<= x < 11745.

576^1289 % 11745 = x = 11016 is the expected answer.

oh interesting!

how do you get that number?

using a calculator:
576^2 % 11745 = 2916
576^3 % 11745 = 81

now we just need to break that huge number down into the "bit sized chucks" above:

lets see 1289 = 3^6 + 3^5 + 3^5 + 3^3 + 3^3 + 3^2 +3^2 + 2


576^1289 % 11745= [(((((576^3)^3)^3)^3)^3)^3 *((((576^3)^3)^3)^3)^3 * ((((576^3)^3)^3)^3)^3 *((576^3)^3)^3 * ((576^3)^3)^3 * (576^3)^3 * (576^3)^3 * 576^2] % 11745

using a table above:

576^1289 % 11745 = [((((81^3)^3)^3)^3)^3 *(((81^3)^3)^3)^3 * (((81^3)^3)^3)^3 *(81^3)^3 * (81^3)^3 * 81^3 * 81^3 * 2916] % 11745

81^3 % 11745 = 2916

576^1289 % 11745 = [(((2916^3)^3)^3)^3 *((2916^3)^3)^3 * ((2916^3)^3)^3 *2916^3 * 2916^3 * 2916 * 2916 * 2916] % 11745

576^1289 % 11745 = [(((2916^3)^3)^3)^3 *((2916^3)^3)^3 * ((2916^3)^3)^3 *2916^9] % 11745

576^1289 % 11745 = [(((2916^3)^3)^3)^3 *((2916^3)^3)^3 * ((2916^3)^3)^3 *(2916^3)^3] % 11745

I won't bother finishing, but you can see we have already crunched it down quite a bit, a couple more of these and it will be manageable.