Number Theory Math Exam

[dropzone]

I was cleaning out my desk and came across an old(2011) final exam from one of my upper level math exams.

Most people only get exposure to math that involves solving equations and stuff but higher level(still undergrad stuff mind you) get more into theory and abstract concepts.

As this was a prereq for the cryptography course and deals with some of the basic concepts used/abused by modern crypto I figure some of you might be interested in seeing what you'll be dealing with if you get into this level of math.



EDIT: For the uninitiated, some characters that you might not know:

The pipe character '|' is used to denote that the first number evenly divides the second number. As in: a|b means a/b is an integer(no decimals).
That little swirl that almost looks like a 'p' is called phi (like sophie without the so) and it refers to Euler's totient function (https://en.wikipedia.org/wiki/Euler's_totient_function) and it is a major part of how RSA works.
The three line equals is for congruency (https://en.wikipedia.org/wiki/Congruence_relation)
The doublestruck Z character refers to the set of all integers, the specific usage is Z/nZ which refers to a Quotient ring (https://en.wikipedia.org/wiki/Quotient_ring)

I don't think there are any other odd characters in there.

[Jake]

Thanks a lot !
Will be kinda helpfull since I have to deal with this stuff for some assignment about crypto.
Do you have the correction laying around ?

[dropzone]

Sorry, I don't have the answers. My answers were stapled to this but they were not attached when I found it so they are probably lost.

Some of these are pretty 'Googleable' or just ask me about them. I may or may not be able to remember how to do everything on here. I remember the core concepts but probably a bit rusty in applying them.

Edit: I added this to the main post, but it also belongs here

Some clarifications on certain characters that wouldn't be easy to google:

The pipe character '|' is used to denote that the first number evenly divides the second number. As in: a|b means a/b is an integer(no decimals).
That little swirl that almost looks like a 'p' is called phi (like sophie without the so) and it refers to Euler's totient function (https://en.wikipedia.org/wiki/Euler's_totient_function) and it is a major part of how RSA works.
The three line equals is for congruency (https://en.wikipedia.org/wiki/Congruence_relation)
The doublestruck Z character refers to the set of all integers, the specific usage is Z/nZ which refers to a Quotient ring (https://en.wikipedia.org/wiki/Quotient_ring)

I don't think there are any other odd characters in there.