See eg. https://en.wikipedia.org/wiki/Salem_number --- the short monograph cited there Salem, R. (1963) "Algebraic numbers and Fourier analysis" is full of fascinating stuff which (AFAIK) is available nowhere else. WFL On 9/13/18, Ed Pegg Jr <ed@mathpuzzle.com> wrote:
At http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html is a list of the 47 smallest known Salem number polynomial.
Here's a list of 47 small numbers. {1, 1, 1, 1, 1, 1, 5, 11, 1, 3, 1, 7, 5, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 13, 19, 5, 1, 1, 13, 5, 1, 7, 1, 1, 41, 1, 1, 3, 19, 1, 1, 1, 1, 5, 3, 7, 1}
If you take the discriminant of the polynomial and divide by the corresponding prime the result is a perfect square number.
--Ed Pegg Jr _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun