Good morning,

Question

Good morning,

Just working through an example but ive gotten stuck and need some help.

So find the least residue of  8^123 Mod 61

So

8^60 = 1 (mod 61)
8^120 = (8^60)^2 = 1^2 = 1 (mod 61)

123 = 2*60+3

So

8^2*60+3 = (8^60)^2 x 8^3
         = 1^2 x 8^3
         = 1 x 512
         = 512

Can anyone please let me know where ive gone wrong. Sorry its the first time ive used this method and im trying to understand it so if you feel you can help without giving the answer away feel free. Im more than happy to work it out myself but I think ive made a mistake here somewhere.

Thank you
Matt

Steve · Answer

well, 512 mod 61 = 24 it's turtles all the way down.

Mat · Answer

Thanks Steve.

Amy ^v^ · Answer

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