The order of inverses mod q

Cristian Cobeli, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review


Let q be a prime number and let a = (a1 , . . . , as) be an s-tuple of distinct integers modulo q. For any x coprime with q, let 1 ≤ x̄ < q be such that x̄x = 1 (mod q). For fixed s and q → ∞ asymptotic formula is given for the number of residue classes x modulo q for which x + a1 < x + a2 < · · · < x + as. The more general case, when q is not necessarily prime and x is restricted to lie in a given subinterval of [1, q], is also treated.

Original languageEnglish (US)
Pages (from-to)87-108
Number of pages22
Issue number1-2
StatePublished - 2000

ASJC Scopus subject areas

  • Mathematics(all)


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