TY - JOUR
T1 - A way to remove duplication from ∑Ni=1 1/xi
AU - Idogawa, Tomoyuki
AU - Tsutsumi, Masayoshi
PY - 1996/8
Y1 - 1996/8
N2 - The main purpose of this paper is to show that we can rewrite a sum of unit fractions ∑Ni = 1 1/xi< 1 in which 0i≤xi+ 1 to the form ∑Ni = 1 1/x′i in which 0 ii+ 1. In other words, it is always possible to remove duplication from ∑Ni = 1 1/xi, without changing its length. Moreover, using this rewriting process, we get a new algorithm for the expansion of Egyptian fractions. We state this algorithm and show some numerical results.
AB - The main purpose of this paper is to show that we can rewrite a sum of unit fractions ∑Ni = 1 1/xi< 1 in which 0i≤xi+ 1 to the form ∑Ni = 1 1/x′i in which 0 ii+ 1. In other words, it is always possible to remove duplication from ∑Ni = 1 1/xi, without changing its length. Moreover, using this rewriting process, we get a new algorithm for the expansion of Egyptian fractions. We state this algorithm and show some numerical results.
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U2 - 10.1006/jnth.1996.0095
DO - 10.1006/jnth.1996.0095
M3 - Article
AN - SCOPUS:0030211040
VL - 59
SP - 215
EP - 224
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
IS - 2
ER -