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The Ruzsa number $R_m$ is defined to be the least integer $r$ such that there is a subset $\\mathcal{A}$ of $\\mathbb{Z}_m$ satisfying $\n1\\le \\sigma_{\\mathcal{A}}(n)\\le r $\nfor any $n\\in \\mathbb{Z}_m$, where $$ \\sigma_{\\mathcal{A}}(n) =\\#\\big\\{(a,a')\\in\\mathcal A^2:\n  a+a'\\equiv n\\pmod{m}\\big\\}. $$ Motivated by a 2024 conjecture of Ding and Zhao, we prove $\n| R_{m+1}-R_m|\\le 144. $ Let $\\mathcal{A}$ be a subset of $\\mathbb{Z}_m$ satisfying $1\\le \\sigma_{\\mathcal{A}}(n)\\le R_m$ for any $n\\in \\mathbb{Z}_m$. 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The Ruzsa number $R_m$ is defined to be the least integer $r$ such that there is a subset $\\mathcal{A}$ of $\\mathbb{Z}_m$ satisfying $\n1\\le \\sigma_{\\mathcal{A}}(n)\\le r $\nfor any $n\\in \\mathbb{Z}_m$, where $$ \\sigma_{\\mathcal{A}}(n) =\\#\\big\\{(a,a')\\in\\mathcal A^2:\n  a+a'\\equiv n\\pmod{m}\\big\\}. $$ Motivated by a 2024 conjecture of Ding and Zhao, we prove $\n| R_{m+1}-R_m|\\le 144. $ Let $\\mathcal{A}$ be a subset of $\\mathbb{Z}_m$ satisfying $1\\le \\sigma_{\\mathcal{A}}(n)\\le R_m$ for any $n\\in \\mathbb{Z}_m$. 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