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Putnam 1973 B5

Source: Putnam 1973

May 25, 2022
Putnamquadraticsalgebrarational functionfunction

Problem Statement

(a) Let zz be a solution of the quadratic equation az2+bz+c=0az^2 +bz+c=0 and let nn be a positive integer. Show that zz can be expressed as a rational function of zn,a,b,c.z^n , a,b,c. (b) Using (a) or by any other means, express xx as a rational function of x3x^{3} and x+1x.x+\frac{1}{x}.
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