User:Goran-Anto Umicevic

I am an enthusiast mathematician with a long time interest (since 1995) for the N-Queens Problem, more specifically on the modular (toroidal) board. It resulted in discovering a simple algorithm that proves: 1) Modular solutions for the n-Queens Problem are possible only if n=p, where p is a prime number 2) "Number of ways of placing n non-attacking toroidal queens on an n X n chessboard", (http://oeis.org/A051906) should be corrected in accordance to a(n)=(n-3)*n, for n=p ... Correct sequence is 1, 0, 0, 0, 10, 0, 28, 0, 0, 0, 88, 0, 130, 0, 0, 0, 238, 0, 304, 0, 0, 0, 460, 0, 0, 0, 0, 0, 754, 0, 868, 0, 0, 0 ..., instead of 1, 0, 0, 0, 10, 0, 28, 0, 0, 0, 88, 0, 4524, 0, 0, 0, 140692, 0, 820496, 0, 0, 0, 128850048, 0, 1957725000, 0, 0, 0, 605917055356, 0, 13404947681712, 0, 0, 0 3) "Number of ways of arranging 2n+1 nonattacking queens on a 2n+1 X 2n+1 toroidal board" (http://oeis.org/A007705) should be supplemented by "if 2n+1=p", that generates same sequence as above

My referent work is here: https://medium.com/@goranumicevic/n-queens-completion-for-n-p-205f6c6397d5

I hope this will be useful for anyone who explores or uses those sequences.

Kind regards, Goran Umicevic