TY - JOUR
T1 - On a problem of Bleicher and Erdös
AU - Yokota, Hisashi
PY - 1988/10
Y1 - 1988/10
N2 - Let D(a, N) = min{nk: a K = ∑1k 1 n1, n1 < n2 < ⋯ < nk, n1 ∈ Z0}, where the minimum ranges over all Egyptian fraction expansions of a N and let D(N) = max{D(a, N): 1 ≤ a < N}. Then D(N) N ≤ (log N)1 + δ(N), δ(N) → 0 as N → ∞, establishing a conjecture of M. N. Bleicher and P. Erdös.
AB - Let D(a, N) = min{nk: a K = ∑1k 1 n1, n1 < n2 < ⋯ < nk, n1 ∈ Z0}, where the minimum ranges over all Egyptian fraction expansions of a N and let D(N) = max{D(a, N): 1 ≤ a < N}. Then D(N) N ≤ (log N)1 + δ(N), δ(N) → 0 as N → ∞, establishing a conjecture of M. N. Bleicher and P. Erdös.
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U2 - 10.1016/0022-314X(88)90017-0
DO - 10.1016/0022-314X(88)90017-0
M3 - Article
AN - SCOPUS:45449125541
SN - 0022-314X
VL - 30
SP - 198
EP - 207
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 2
ER -