A Sharp Bound for a Shifted GCD Sum over Divisors
Year: 2026
Type: preprint
Abstract: For every integer n >= 2, defineA(n) = sum_{d|n} gcd(d-1, n/d-1).We prove the sharp inequality A(n) <= 9n/4. Equality holds if and onlyif n = 36. The argument is elementary apart from an exact finiteverification for 2 <= n <= 1,340,963; complete source code for thatverification is supplied. We also record a reformulation as a restrictedshifted gcd sum modulo n-1.
Author: Hirsch, Krystal
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208820356
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