There are formulas for counting the number of representations of a positive integer $N$ as a sum of three integer squares. What is a reference for $$ \#\{(x,y,z)\in \mathbf{N}^3: 5^4 x^2+y^2+z^2=N\} ?$$
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4$\begingroup$ and what is it? $\endgroup$– Max HornSep 27 at 16:49
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1$\begingroup$ Another source that may give some ideas is math.stackexchange.com/questions/1972120/… $\endgroup$– Gerry MyersonOct 3 at 2:40
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1$\begingroup$ International Journal of Number Theory Vol. 17, No. 03, pp. 547-575 (2021) Local densities of diagonal integral ternary quadratic forms at odd primes by Edna Jones, doi.org/10.1142/S1793042120400357 seems more helpful. The abstract says the paper contains formulas which "can be used to compute the representation numbers of certain ternary quadratic forms." See also services.math.duke.edu/~elj31/talks/… $\endgroup$– Gerry MyersonOct 3 at 2:45
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1$\begingroup$ Golubeva, E.P. Representation of numbers, divisible by a large square, by positive ternary quadratic forms. J Math Sci 43, 2519–2530 (1988), doi.org/10.1007/BF01374981 looks relevant. $\endgroup$– Gerry MyersonOct 3 at 2:50
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1$\begingroup$ Hello, this is amazing, thanks! Edna Jones' paper is exactly what I was looking for. $\endgroup$– Dr. PiOct 4 at 8:39
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1 Answer
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You may refer to Theorem 13 of the paper 'On the Number of Representations of Integers by various Quadratic and Higher Forms' by Nikos Bagis and M.L Glasser. (paper)
