Remarks on the "greedy Obd" Egyptian Fraction Algorithm
نویسنده
چکیده
Fibonacci, in 1202 ([8], see also [1], [7]) introduced the greedy algorithm: we take the greatest Egyptian fraction 1 / xx with l/xl < a/b, form the difference a/b-l/xl=:al/bl [where (ax, bx) = 1] and, if allbl is not zero, continue similarly. It is easily seen that the sequence of numerators aQ: = a, al9 a2,... is strictly decreasing, from which it follows that after finitely many, say s, steps (s<a), the process will stop. This gives us a representation | = ±+...+J_, ,<„<...<,,. (,.2)
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