1. V

    Fibonacci generating functions for pair/impair indexes.

    Let f_n be the sequence of Fibonacci numbers. It's known that \sum_{n \ge 0} f_n x^n = \dfrac{1}{1-x-x^2} What is the interpretation of this for \sum_{n \ge 0} f_{2n} x^n \text{ and }\sum_{n \ge 0} f_{2n+1} x^n\text{ ?} How do we prove it?
  2. F

    Proof or relationship between generalised entropy and Atkinson indexes

    Hi, see attached this difficult proof in pdf format. This result can be shown to be correct computationally, but is there an analytic solution? Any guidance would be most appreciated. Edit: see also these additional identities that may be useful.
  3. S

    Groups, subgroups and indexes

    Here is a problem I think I have a solution for, I am just not 100% sure on one of the detail Let G be a group that does not have a subgroup of index 2. Show that every subgroup of index 3 is normal in G My proof Let H\leq G, [G:H]=3, first we will assume that H is not trivial (if it is...
  4. A

    P-Sylow subgroups, Normalizers, Indexes

    Let G be a group. Prove that G has no P-Sylow subgroup 'H' for which [G:N(H)]=2. For every subgroup H in G, the Normalizer is defined as N(H):={ g\in G: gH=Hg } I need to find a way to prove this. If |G| is infinity, then for every prime p and natural m, we get that |G| is never m*p^n ...
  5. K

    Primative roots and indexes

    Let g be a primative root of m. An index of a number a to the base g (written ind_{g}a) is a number t such that g^{t} \equiv a \ (mod\ m). Given that a \equiv b\ (mod\ m) and that g is a primative root modulo m, prove the following assertions: i. ind_{g}ac \equiv ind_{g}a + ind_{g}c\ \{mod\...
  6. N

    Mapping arrays to use negative indexes

    For an assignement in my Continuous Time Signals class, we were asked to calculate the fourier series of a given x(t). The problem I'm running into is we are asked to calculate the Dn in my m-file from -10 to 10 (course Matlab cannot handle negative indices and 0 since the numerical values of...
  7. E

    Formula to calculate indexes from row and column

    This is as much about programming as it is software, but I thought there might be a nifty way to do it with excel that I'm unaware of. I have two sets of numbers, indexes for rows and columns, and I need to map them to indexes. Rather than actually setting the cell values, I'm trying to get...