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### What are some books that are in the spirit of David A. Cox' “Primes of the Form $x^2+ny^2$”

David A. Cox "Primes of the Form $x^2+ny^2$: Fermat, Class Field Theory, and Complex Multiplication." has a very good (at least to me, and many) methodology. He starts from page 1 asking a simple ...
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### Classification of the positive integers not being the sum of four non-zero squares

It is well known that every positive integer is the sum of at most four perfect squares (including $1$). But which positive integers are not the sum of four non-zero perfect squares ($1$ is still ...
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### How to prove that the roots of this equation are integers?

Let there be an equation $a^2 + 4ab + b^2 - 121 = 0$ where I want to prove that a,b are integers. Then I want to find whether there are integer values of $b$ for which $a$ is also an integer. Let us ...
I am looking for integer solutions to the equation $$x^2 = 5y^2 + 14y + 1$$ I know that Pell's Equation is of the form $x^2 - ny^2=1$ and that there exist algorithms to solve this equation. I was ...