Kai Jin

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 23, 2017, Number 1, Pages 24—27

**Download full paper: PDF, 128 Kb**

## Details

### Authors and affiliations

Kai Jin

*Institute for Interdisciplinary Information Sciences
Tsinghua University
Beijing 100084, China
*

### Abstract

We consider the problem of partitioning the numbers 1..*n* to ascending sequences as few as possible, so that every neighboring pair of elements in each sequence add up to some perfect square number. We prove that the minimum number of sequences is . We hope that this paper exhibits an interesting property of the perfect square numbers.

### Keywords

- Perfect square number
- Elementary Number theory
- Sequences

### AMS Classification

- 11B75
- 11B83

### References

- Anonymous, Arranging numbers from 1 to
*n*such that the sum of every two adjacent numbers is a perfect power, www.mathoverflow.net, 2015, http://mathoverflow.net/questions/199677/. - Anonymous, Problems & Puzzles: Puzzle 311. Sum to a cube, www.primepuzzles.net, http://www.primepuzzles.net/puzzles/puzz_311.htm.

## Related papers

## Cite this paper

APAJin, K. (2017). Ascending sequences with neighboring elements add up to perfect square numbers. Notes on Number Theory and Discrete Mathematics, 23(1), 24-27.

ChicagoJin, Kai. “Ascending Sequences with Neighboring Elements Add up to Perfect Square Numbers.” Notes on Number Theory and Discrete Mathematics 23, no. 1 (2017): 24-27.

MLAJin, Kai. ”Ascending Sequences with Neighboring Elements Add up to Perfect Square Numbers.” Notes on Number Theory and Discrete Mathematics 23.1 (2017): 24-27. Print.