ON THE NUMBER OF DIVISORS OF n2 - 1

Adrian W. Dudek

doi:10.1017/S0004972715001136

ON THE NUMBER OF DIVISORS OF n² - 1

Adrian W. Dudek^*

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

We prove an asymptotic formula for the sum ∑_n≤N d(n² - 1), where d(n) denotes the number of divisors of n. During the course of our proof, we also furnish an asymptotic formula for the sum ∑_d≤N g(d), where g(d) denotes the number of solutions x in ℤ_d to the equation x² ≡ 1 (mod d).

Original language	English
Pages (from-to)	194-198
Number of pages	5
Journal	Bulletin of the Australian Mathematical Society
Volume	93
Issue number	2
DOIs	https://doi.org/10.1017/S0004972715001136
Publication status	Published - 1 Apr 2016

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abstract = "We prove an asymptotic formula for the sum ∑n≤N d(n2 - 1), where d(n) denotes the number of divisors of n. During the course of our proof, we also furnish an asymptotic formula for the sum ∑d≤N g(d), where g(d) denotes the number of solutions x in ℤd to the equation x2 ≡ 1 (mod d).",

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AB - We prove an asymptotic formula for the sum ∑n≤N d(n2 - 1), where d(n) denotes the number of divisors of n. During the course of our proof, we also furnish an asymptotic formula for the sum ∑d≤N g(d), where g(d) denotes the number of solutions x in ℤd to the equation x2 ≡ 1 (mod d).

KW - Diophantine quintuples

KW - arithmetic functions

KW - asymptotic estimate

KW - divisor sum

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JF - Bulletin of the Australian Mathematical Society

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ON THE NUMBER OF DIVISORS OF n² - 1

Abstract

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