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  "body": "\n## Statement\n\nLet $F_k$ be the [[Fibonacci numbers|0GA9K57A39]], and let $N$ be a positive integer.\nThen there is a unique finite set $\\{c_1, \\dots, c_r\\}$ of integers, with $r \\ge 1$, such that\n$$N = F_{c_1} + F_{c_2} + \\dots + F_{c_r},$$\neach $c_i \\ge 2$, and $c_{i+1} \\ge c_i + 2$ for $1 \\le i \u003c r$.\n\n## Remarks\n\nThe condition says that the sum uses distinct Fibonacci numbers and no two consecutive ones. The bound $c_i \\ge 2$ excludes $F_0 = 0$ and the repeated value $F_1 = F_2 = 1$.\nExample: $100 = 89 + 8 + 3 = F_{11} + F_6 + F_4$.\nThe greedy method finds the representation: subtract the largest Fibonacci number that is at most $N$, and repeat.\n\n## Explanations\n\n### L1 human\n\nEach positive integer is a sum of different Fibonacci numbers, no two of them neighbours in the sequence, in exactly one way.\nFor example, $20 = 13 + 5 + 2$.\n",
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  "msc": [
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  "name": "Zeckendorf's theorem",
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