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The celebrated Erd\\H{o}s-Tur\\'{a}n conjecture says that, if $R_A(n)\\ge 1$ for all sufficiently large integers $n$, then the representation function $R_A(n)$ cannot be bounded. For any positive integer $m$, Ruzsa's number $R_m$ is defined to be the least positive integer $r$ such that there exists a set $A\\subseteq \\mathbb{Z}_m$ with $1\\le R_A(n)\\le r$ for all $n\\in \\mathbb{Z}_m$. 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The celebrated Erd\\H{o}s-Tur\\'{a}n conjecture says that, if $R_A(n)\\ge 1$ for all sufficiently large integers $n$, then the representation function $R_A(n)$ cannot be bounded. For any positive integer $m$, Ruzsa's number $R_m$ is defined to be the least positive integer $r$ such that there exists a set $A\\subseteq \\mathbb{Z}_m$ with $1\\le R_A(n)\\le r$ for all $n\\in \\mathbb{Z}_m$. 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