Authors and affiliations
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.
- Perfect square number
- Elementary Number theory
- 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.
Cite this paperAPA
Jin, K. (2017). Ascending sequences with neighboring elements add up to perfect square numbers. Notes on Number Theory and Discrete Mathematics, 23(1), 24-27.Chicago
Jin, 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.MLA
Jin, 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.