Yesterday, I challenged you to prove that
where ,
, and the
are defined by
and
.
The proof is by induction on . The base case
is just arithmetic:
Now suppose that we already know the statement holds for some particular ; we must show that it also holds for
. The proof is not too hard, but we have to handle the stacked exponents with care! (Note also that all the following equalities are really taken
, which is OK since addition, subtraction, and multiplication are all compatible with taking remainders.)
(The last step is because we know from yesterday that .) So
, which is what we wanted to show.
Here it is proved not only the equality mod M_n, but it is also proved the equality in general. Am I right?
Well, we defined the s_n in terms of mod M_n in the first place. I will write more about this today.
Ok. Thanks.
Hendrix College is a University or a high-school? What can we study there, high-school subjects or universitary careers?
The terminology can be confusing since it is used very differently depending on what country you are in. Hendrix is definitely not a high school, it is a 4-year school that a student would attend after completing high school. It is not a university though, the difference being that it is relatively small and does not offer graduate degrees like a master’s degree or PhD.
Ok, thanks for your answer, friend!
Pingback: MaBloWriMo 8: definition of s and mod | The Math Less Traveled
So, here are studied professional careers, but with a duration of 4 years. What careers are studied here, for instance?
I suggest you just go poke around https://www.hendrix.edu/ , I think you will be able to find answers to your questions much more quickly that way than I would be able to answer them. For example there is a list of the academic programs here: https://www.hendrix.edu/academics/majorsandminors/
Thank you!
I had visited that site, but I hadn’t reviewed the academics section.
Pingback: MaBloWriMo 21: the order of omega, part I | The Math Less Traveled