Sums of Consecutive Integers

2007/01/04 by Wai Yan Pong, Pong, Wai Yan
Mathematics · #01A99 #11A99 #Advanced Combinatorial Mathematics #Analytic Number Theory Research #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #Number Theory (math.NT) #math.HO #math.NT #msc:01A99 #msc:11A99

paper · pdf · doi:10.48550/arxiv.math/0701149

7 pages, 1 table, 3 figures. To appear in the College Journal of Mathematics, March 2007

arxiv created 2007/01/04 · openalex publication_date 2007/01/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A decomposition of a natural number n is a sequence of consecutive natural numbers that sums to n. We construct a one-to-one correspondence between the odd factors of a natural number and its decompositions. We study the decompositions by their lengths and introduce the concept of length spectrum. Also, we use diagrams to illustrate the ideas behind our proofs.

Related

• A theorem about partitioning consecutive numbers
• On sums of triangular numbers
• A Short Proof of a Known Relation for Consecutive Power Sums
• q-analogues of the sums of powers of consecutive integers
• On the Sum of Consecutive Primes