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  "body": "\n## Definition\n\nLet $G$ be an [[abelian group|082GHNPJ53]], for example $\\Z$, and let $A$ be a subset of $G$.\nThe set $A$ is a *Sidon set* if for all $a, b, c, d \\in A$ with $a + b = c + d$, one has $\\set{a, b} = \\set{c, d}$.\n\n## Remarks\n\nIf $G$ has no elements of order $2$, as in $\\Z$, the definition is equivalent to this one: the differences $a - b$ with $a, b \\in A$ and $a \\ne b$ are pairwise different.\nThe set $\\set{1, 2, 4, 8}$ is a Sidon set in $\\Z$.\nIts sums $a + b$ with $a \\le b$ are $2, 3, 4, 5, 6, 8, 9, 10, 12, 16$, and these ten numbers are distinct.\nThe set $\\set{1, 2, 3, 4}$ is not a Sidon set, since $1 + 4 = 2 + 3$ but $\\set{1, 4} \\ne \\set{2, 3}$.\nAn infinite Sidon set of positive integers, listed in increasing order, is called a Sidon sequence.\nSidon sets in $\\Z$ are also called Golomb rulers when they are finite.\n",
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