On ternary Egyptian fractions with prime denominator
نویسندگان
چکیده
منابع مشابه
Egyptian Fractions with Each Denominator Having Three Distinct Prime Divisors
Any natural number can be expressed as an Egyptian fraction, i.e., P 1/ai with a1 < a2 < · · · < a`, where each denominator is the product of three distinct primes.
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In this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. We prove that if $N$ is a weakly prime subtractive ternary subsemimodule of a ternary $R$-semimodule $M$, then either $N$ is a prime ternary subsemimodule or $(N : M)(N : M)N = 0$. If $N$ is a $Q$-...
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It is well known that the ancient Egyptians represented each fraction as a sum of unit fractions – i.e., fractions with unit numerators; this is how they, e.g., divided loaves of bread. What is not clear is why they used this representation. In this paper, we propose a new explanation: crudely speaking, that the main idea behind the Egyptian fractions provides an optimal way of dividing the loa...
متن کاملBinary Egyptian Fractions
Let Ak*(n) be the number of positive integers a coprime to n such that the equation a n=1 m1+ } } } +1 mk admits a solution in positive integers (m1 , ..., mk). We prove that the sum of A2*(n) over n x is both >>x log 3 x and also <<x log x. For the corresponding sum where the a's are counted with multiplicity of the number of solutions we obtain the asymptotic formula. We also show that Ak*(n)...
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ژورنال
عنوان ژورنال: Research in Number Theory
سال: 2019
ISSN: 2522-0160,2363-9555
DOI: 10.1007/s40993-019-0172-z