PROPORTION PATTERNS WITH BINOMIALS

Far East Journal of Mathematical Education 2026

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Authors: Mihai Caragiu
DOI: 10.17654/0973563126005
Cited by: 0

Abstract

We prove that the only occurrence of consecutive binomial coefficients in the proportion is 1001, 2002, 3003 - corresponding to and . Then we further extend this result to proportions of three consecutive binomials, where is an integer. On the other hand, we prove that for any integer , there is no pattern of binomials in the proportion .

Fields of Study & Subjects

Analytic Number Theory Research Advanced Combinatorial Mathematics Advanced Mathematical Identities

Publication details

Journal / source
Far East Journal of Mathematical Education
Volume
28
Issue
1
Pages
31–37
Publication date
10 January 2026