2020/01/10 by Sid Ali Bousla, Bousla, Sid Ali, Bakir Farhi +1
Computer Science · Engineering · Mathematics · #11B83 #30B40 #33B15 #Advanced Mathematical Theories #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Primary 11A05 #Secondary 13G05 #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2001.03374
openalex publication_date 2020/01/10 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
This paper is devoted to studying the numbers Lc,m,n :=\n\lcm m2+c ,(m+1)2+c , \… , n2+c , where c,m,n are positive\nintegers such that m \≤ n. Precisely, we prove that Lc,m,n is a\nmultiple of the rational number\n\
frac
displaystyle
prodk=mn
left(k2+c
right)c
cdot\n(n-m)!
displaystyle
prodk=1n-m
left(k2+4c
right) , and we derive (as\nconsequences) some nontrivial lower bounds for Lc,m,n. We prove for\nexample that if n- \(1)/(2) n2/3 \≤ m \≤ n, then we have Lc,m,n\n\≥ \λ(c) \⋅ n e3 (n - m), where \λ(c) := frace- \(2\n\π2)/(3) c - \(5)/(12)(2 \π)3/2 c. Further, it must be noted that\nour approach (focusing on commutative algebra) is new and different from those\nusing previously by Farhi, Oon and Hong.\n