Sums of Consecutive Integers
classification
🧮 math.HO
math.NT
keywords
naturalconsecutivedecompositionsnumbersumsbehindconceptconstruct
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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.
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