Proof of the Modulo 4 Conjecture for OEIS A141117 and of the Parity Conjecture for OEIS A091713
Year: 2026
Type: preprint
Abstract: Let πΉ(π₯) be the ordinary generating function of OEIS A091713, determined by πΉ(π₯) = π₯ + π₯πΉβ¦3(π₯),and let π΄(π₯) = πΉβ¦2(π₯), the ordinary generating function of OEIS A141117. We prove that every coefficientof πΉ is odd and that, for π > 1, the coefficient π(π) = [π₯π] π΄(π₯) is divisible by 4 exactly when 3 | π, whileπ(π) β‘ 2 (mod 4) otherwise. The argument is entirely within rings of formal power series.1 Statement and conventionsLet πΉ(π₯) β π₯Z[[π₯]] be the ordinary generating function of OEIS A091713. Its defining fu
Author: Yuan, Chi
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203947899
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