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Wrong results with "mod"

Asked by Matthew Durkin on 10 Feb 2019
Latest activity Answered by John D'Errico
on 10 Feb 2019
Why does Matlab give me the wrong answer to mod(14^27,55) = 32, it should equal 9. What am I doing wrong?

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Never mind, I found out I need to use "powermod" to get the answer.
Maybe you should copy your comment to an answer, and accept it.

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1 Answer

Answer by John D'Errico
on 10 Feb 2019

This fails because MATLAB cannot represent an integer larger than 2^53-1 as an exact integer, when working in double precision.
14^27 is far larger than that of course. So it fails. This leaves you with two basic options, to use symbolic arithmetic, (or perhaps my VPI toolbox) or to use powermod.
mod(sym(14)^27,55)
ans =
9
powermod(14,27,55)
ans =
9
The powermod solution is better of course, in the sense that the huge number 14^27 never had to be fully computed.

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