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VARIANTS OF ERDŐS–SELFRIDGE SUPERELLIPTIC CURVES AND THEIR RATIONAL POINTS
Author(s) -
Das Pranabesh,
Laishram Shanta,
Saradha N.
Publication year - 2018
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579317000559
Subject(s) - mathematics , prime (order theory) , interval (graph theory) , combinatorics
For the superelliptic curves of the form( x + 1 ) … ( x + i − 1 ) ( x + i + 1 ) … ( x + k ) = y lwith y ≠ 0 , k ⩾ 3 , ℓ ⩾ 2 , a prime and for i ∊ [ 2 , k ] ∖ Ω , we show that ℓ < e 3 k . Here Ω denotes the interval [ p θ , ( k − p θ ) ) , where p θ is the least prime greater than or equal to k / 2 . Bennett and Siksek obtained a similar bound for i = 1 in a recent paper.