tildedave / go-finite-fields Goto Github PK

I have been playing with this library and I found the following results which I wanna make sure I interpret right:

FactorBerlekamp([-26, 0, 1], 2) returns []
FactorBerlekamp([-26, 0, 1], 3) returns []
FactorBerlekamp([-26, 0, 1], 5) returns [[4, 1], [1, 1]]

The first two results I seem to interpret as they can't be factored but $x^2 - 26 = x^2 mod 2$ which can be factored as $(x)(x)$ but maybe that isn't too bad as it is supposed to be a square free polynomial. and for mod 3, $x^2 - 26 = x^2 - 2 mod 3$ which seems to be irreductible so it makes sense.

Are my thoughts correct?