Binary Egyptian Fractions
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چکیده
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)<<n :k+= where :k is defined recursively by :2=0 and :k=1&(1&:k&1) (2+:k&1). 2000 Academic Press
منابع مشابه
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تاریخ انتشار 1999