Wrong results with "mod"

Why does Matlab give me the wrong answer to mod(14^27,55) = 32, it should equal 9. What am I doing wrong?

[Matthew Durkin]

Never mind, I found out I need to use "powermod" to get the answer.

[the cyclist]

Maybe you should copy your comment to an answer, and accept it.

Answer 1

[John D'Errico]

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.