Computing mth roots

Keith Matthews, Computing m-th roots, The College Mathematics Journal 19 (1988) 174-176.
(A discrete version of Newton's method which gives the integer part of (p/q)^1/m.
Also see H. Lüneburg's book On the Rational Normal Form of Endomorphisms 1987, B.I. Wissenschaftsverlag, Mannheim/Wien/Zürich.
See the BCMATH implementation of BABY_MTHROOT and the BC version.
Harley Flanders supplied the idea of using equation (4) below.

Corrections

(28/12/2022): On line -1, p. 175, replace "in base" by "with"
In the proof of the Lemma, the phrase "But c > x implies" should be replaced by "But c < x implies".

Email
http://www.numbertheory.org/keith.html
31st July 2026