MathDB

B5

Part of 1973 Putnam

Problems(1)

Putnam 1973 B5

Source: Putnam 1973

5/25/2022
(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}.
Putnamquadraticsalgebrarational functionfunction