Remarks on the “Greedy Odd” Egyptian Fraction Algorithm II
| Autor: | Pihko, Jukka |
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| Zdroj: | The Fibonacci Quarterly; August 2010, Vol. 48 Issue: 3 p202-208, 7p |
| Abstrakt: | AbstractLet a, bbe positive, relatively prime integers with a< band bodd. Let 1/x1be the greatest Egyptian fraction with x1odd and 1/x1≤ a/b. We form the difference a/b− 1/x1=: a1/b1(with gcd(a1, b1) = 1) and, if a1/b1is not zero, continue similarly. Given an odd prime pand 1 < a< p, we prove the existence of infinitely many odd numbers bsuch that gcd(a, b) = 1, a< b, and the sequence of numerators a0:= a, a1, a2, … is a, a+ 1, a+ 2, …, p− 1, 1. |
| Databáze: | Supplemental Index |
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