Find all pairs $\displaystyle (x,y) \in \mathbb{N}^2$ with $\displaystyle x^2+3y^2=364$
Was unable to get the lecture notes for this type of question. Could someone possibly walk me through this problem? Thanks you.
You don't need any lecture notes for this, it's just a matter of checking the possible values. You know that x and y are whole numbers, and y must be at most 11, because 3×11²=363, which is nearly 364. In fact, that gives you your first solution: $\displaystyle x=1,\ y=11$. Now just check whether $\displaystyle 364-3y^2$ is a perfect square, for y=1,2,...,10. That will pick up any other solutions.