Recent content by cyclic

  1. C

    Number of Subgroups of Index m

    Perhaps we can use congruence subgroups here? Or perhaps we can study SL(2,Z) using its action on the projective line over the integers modulo n? I'm pretty stumped and would appreciate any help.
  2. C

    Number of factors of a polynomial in F_2

    Apologies, I realized that I typed the question wrong. Thank you for the response, though. I've edited the question. Looking at the factorizations in Mathematica, I'm not sure that a general factorization exists, but I may be wrong.
  3. C

    Number of factors of a polynomial in F_2

    This is a pattern I noticed when playing around with Mathematica. Is there any way to rigorously prove this? I was not able to find any literature concerning the number of factors in a finite field, especially because this is called a "pentanomial" in said literatures. These don't have much...