Calculating the first m + 1 partial quotients of the unique positive root of a trinomial axn + bxn-1 + c

We are dealing with polyomial f(x)=axn + bxn-1 + c with integer coefficients, a > 0, c < 0. This will have a unique positive root α which we will assume is greater than 1.
The method of Lagrange (1797) is used to find the the first m + 1 partial quotients of α.

References

  1. Number Theory with Computer Applications, R. Kumanduri and C. Romero, Prentice Hall 1997, page 261
  2. Elements of Computer Algebra with Applications, A.G. Akritas, Wiley 1989, 333-399.
  3. Art of computer programming, volume 2, D.E. Knuth, problem 13, Ch. 4.5.3.
  4. Continued fractions for some algebraic numbers, S. Lang and H. Trotter, J. für Math. 255 (1972) 112-134; Addendum 267 (1974) ibid. 219-220.
  5. A new proof of Vincent's theorem, A. Alesina, M. Galuzzi, L'Enseignement Math 44 (1988), 219-256.
  6. An explanation of some exotic continued fractions found by Brillart, H.M. Stark, Computers in number theory, Academic Press 1971, 21-35.
For a program that develops the continued fraction of all real roots of a suitably general polynomial, see CALC.

Enter a (≠ 0):
Enter b :
Enter c (ac < 0):
Enter n (1 < n ≤ 100):
Enter m (0 ≤ m < 1000):

Last modified 21st July 2006
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