On the maximal difference between an element and its inverse modulo n

On the maximal difference between an element and its inverse modulo n
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DOI:
10.1023/b:mahu.0000010815.14847.96
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发表时间:
2003-09
影响因子:
0.8
通讯作者:
Mizan R. Khan;I. Shparlinski
Mizan R. Khan;I. Shparlinski
中科院分区:
数学4区
文献类型:
--
作者:
Mizan R. Khan;I. Shparlinski

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We derive a lower bound for the arithmetic function M (n)= max {| a-b|: a, b∈ ℤ n and ab≡ 1 (mod n)} which then gives the asymptotic n-M (n)= o (n. 75+ ε) for any ε> 0.