Asymptotic analysis reveals the relationship between representations of integers as two squares.
We derive the following asymptotic formula ∑'n xr(n)/r(n+1) = x(log x)-3/4(c+o(1)), x → +∞, where $r(n)$ is the number of representations of n as a sum of two squares, c is a positive constant, and the prime indicates summation over those n for which r(n+1)≠ 0.
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Vitalii V. Iudelevich (2026) studied this question.
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