Add Zeckendorf in Every Language Article

sources/projects/zeckendorf/description.md

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+[Edouard Zeckendorf][3] was a Belgian amateur mathematician who proposed a
+[Theorem][1] that states that every non-negative integer (_N_) can be
+represented as a sum of distinct non-consecutive [Fibonacci Numbers][2]. In
+other words,
+
+* _N_ = _F_<sub>_c_<sub>1</sub></sub> + _F_<sub>_c_<sub>2</sub></sub> + ... + _F_<sub>_c_<sub>_n_</sub></sub>
+
+where:
+
+* _F_<sub>_k_</sub> is the _k_ th Fibonacci number
+* _c_<sub>_i_</sub> &ge; 2
+* _c_<sub>_i_ + 1</sub> &gt; _c_<sub>_i_</sub> + 1
+
+Each Fibonacci number (_F_<sub>_k_</sub>) is the sum of the previous two Fibonacci
+numbers:
+
+* _F_<sub>0</sub> = 0
+* _F_<sub>1</sub> = 1
+* _F_<sub>2</sub> = _F_<sub>1</sub> + _F_<sub>0</sub> = 0 + 1 = 1
+* _F_<sub>3</sub> = _F_<sub>2</sub> + _F_<sub>1</sub> = 1 + 1 = 2
+* ...
+* _F_<sub>_k_</sub> = _F_<sub>_k_ - 1</sub> + _F_<sub>_k_ - 2</sub>
+
+This relationship is the reason why non-consecutive Fibonacci numbers are used.
+
+To find the Fibonacci numbers that add up to _N_:
+
+* Find all the Fibonacci numbers up to and including _N_, starting at
+  _F_<sub>2</sub>.
+* Going from largest to smallest, select each Fibonacci number such that the
+  sum of this value plus all the prior selected values is less than or equal to
+  _N_.
+
+For example, for _N_ = 67, these are the Fibonacci numbers up to 67:
+
+* 1, 2, 3, 5, 8, 13, 21, 34, 55
+
+Select the appropriate Fibonacci numbers:
+
+| Trial Sum   | Fibonacci Number | Selected |
+| :---------: | :--------------: | :------: |
+| 0           | 55               | &#9989;  |
+| 55          | 34               |          |
+| 55          | 21               |          |
+| 55          | 13               |          |
+| 55          | 8                | &#9989;  |
+| 63          | 5                |          |
+| 63          | 3                | &#9989;  |
+| 66          | 2                |          |
+| 66          | 1                | &#9989;  |
+
+Therefore, using the selected numbers, _N_ can be represented as:
+
+* 67 = 55 + 8 + 3 + 1
+
+A possible optimization for this procedure would be to skip Fibonacci
+numbers that are consecutive to the last selected value and to terminate
+the loop as soon as the sum equals to _N_.
+
+[1]: https://en.wikipedia.org/wiki/Zeckendorf%27s_theorem
+[2]: https://en.wikipedia.org/wiki/Fibonacci_sequence
+[3]: https://en.wikipedia.org/wiki/Edouard_Zeckendorf

sources/projects/zeckendorf/requirements.md

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+Create a file called "Zeckendorf" using the naming convention appropriate for
+your language of choice.
+
+Write a sample program that accepts a single non-negative integer from the
+command line and outputs a comma-separated list of Fibonacci numbers whose
+sum equals the specified value. For zero, output an empty list. If the command
+line argument is missing or not a non-negative integer, output the error
+message specified in the [Testing](#testing) section.