Given a length , is it possible to construct a set of integers such that each
as a proper divisor? This is Znám’s problem.
This problem has solutions for , and all solutions for have been found, and a few for higher are known. The Sylvester sequence provides many of the solutions. At Wayne University in 2001, Brenton and Vasiliu devised an algorithm to exhaustively search for solutions for a given length, and thus they found all solutions for . Their algorithm, though smarter than a brute force search, is still computationally intense the larger gets.
The problem is believed to have been first posed by Štefan Znám (http://planetmath.org/VStefanZnam) in 1972. Qi Sun proved in 1983 that there are solutions for all .
Brenton, L, and Vasiliu, A. “Znam’s Problem.” Math. Mag. 75, 3-11, 2002.
|Date of creation||2013-03-22 15:47:39|
|Last modified on||2013-03-22 15:47:39|
|Last modified by||Mravinci (12996)|