Denser Egyptian Fractions
نویسنده
چکیده
An Egyptian fraction is a sum of reciprocals of distinct positive integers, so called because the ancient Egyptians represented rational numbers in that way. In an earlier paper, the author [8] showed that every positive rational number r has Egyptian fraction representations where the number of terms is of the same order of magnitude as the largest denominator. More precisely, there exists a positive constant C(r) such that for every x that is sufficiently large in terms of r, there is a set E of positive integers not exceeding x with ∑
منابع مشابه
. N T ] 8 A pr 1 99 8 DENSE EGYPTIAN FRACTIONS
Every positive rational number has representations as Egyptian fractions (sums of reciprocals of distinct positive integers) with arbitrarily many terms and with arbitrarily large denominators. However, such representations normally use a very sparse subset of the positive integers up to the largest denominator. We show that for every positive rational there exist representations as Egyptian fr...
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