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I came with a curious question, that I tried solving in $\mathbb{Z^3}$, the equation $2x^2 + 3y^2 + 5z^2 = R$, for $R > 0 $, where $n(R)$ is the quant. of triples that satisfy that equation. What I tried was to calculate the following:

$$\lim_{R \to \infty} \frac{n(1)+n(2)+...n(R)}{R^{3/2}} $$

However I came with a problem, I didn't know how to know the number of solutions for each and every number $R$, and I think that would also complicate the problem, and I think there is a better way to take this limit.

João Víctor Melo
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  • See https://math.stackexchange.com/questions/4349520/determine-value-of-a-limit-envolving-integer-solutions-x-y-z-to-2x23y25 - no answer there, but plenty of comments. – aschepler Feb 02 '22 at 21:57

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