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It can be shown that the total number of solutions in $[n]$ to the Sidon equation is $n^3/12 + O(n^2)$ and so, trivially, $AR_{X+Y = Z + T}^k (n) \\leq n^3 /12 + O (n^2)$. We improve this upper bound to \\[ AR_{X+Y = Z+ T}^k (n) \\leq \\left( \\frac{1}{12} - \\frac{1}{24k} \\right)n^3 + O_k(n^2) \\] for all $n \\geq k \\geq 4$. 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