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

Mizan R. Khan; Igor E. Shparlinski

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

Mizan R. Khan^*, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	111-117
Number of pages	7
Journal	Periodica Mathematica Hungarica
Volume	47
Issue number	1-2
Publication status	Published - 2003

Cite this

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abstract = "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.",

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AU - Khan, Mizan R.

AU - Shparlinski, Igor E.

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AB - 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.

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JF - Periodica Mathematica Hungarica

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

Abstract

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