I have seen this problem a long time ago. It is really supprising, maybe you shall like it as well.
Given any non-empty set we can define a binary operation on this set to turn it into a group.
For what values does \mathbb{Z}[\zeta] have unique factorization?
I know Kummer shown that \zeta being a 23-rd root of unity fails to have unique factorization.
Consider the Diophantine equation:
y^3 = x^2 + 2
Without using rational elliptic curves and unique factorization in \mathbb{Z}[\sqrt{-2}] how many different ways can you show that this equation has only a single solution.
Historical question: Who was the mathematician who created the...
I am sure this has been discussed a lot here since this is a physics forum.
But I want to make a list of what I think is good if you want to learn them.
Elementary
1)Partial Differential Equations and Boundary Value Problems with Fourier Series. This book is as simple as it gets. So even...