# Thread: What is Number Theory?

1. ## What is Number Theory?

I have a possibilty of taking number theory in the spring and am unsure of what this course entails. Also, would this be a good course to take if I'm considering grad school?

2. Originally Posted by kathrynmath
I have a possibilty of taking number theory in the spring and am unsure of what this course entails. Also, would this be a good course to take if I'm considering grad school?
Number theory is the properties of integers themselves. Thus, you deal with equations and theorems only about integers. For example, how do you find all positive solutions to $\displaystyle 2x + 5y + 11z = 2000$, where $\displaystyle x,y,z$ are integers? Or how do you prove that $\displaystyle x^4+y^4 = z^4$ has no positive solution? You would also talk about prime numbers, since integers can be broken up into primes. And do more theorems about primes. If that would interest you then you can take the course.

As far as a graduate course goes what I wrote above would be an undergraduate topic. Since it is elementary, no advanced mathematical methods.