Sums of Consecutive Integers
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- January 2007
- DOI:
- 10.48550/arXiv.math/0701149
- arXiv:
- arXiv:math/0701149
- Bibcode:
- 2007math......1149P
- Keywords:
-
- Mathematics - History and Overview;
- Mathematics - Number Theory;
- 01A99;
- 11A99
- E-Print:
- 7 pages, 1 table, 3 figures. To appear in the College Journal of Mathematics, March 2007