MathDB

B5

Part of 1986 Putnam

Problems(1)

Putnam 1986 B5

Source:

8/5/2019
Let f(x,y,z)=x2+y2+z2+xyzf(x,y,z) = x^2+y^2+z^2+xyz. Let p(x,y,z),q(x,y,z)p(x,y,z), q(x,y,z), r(x,y,z)r(x,y,z) be polynomials with real coefficients satisfying f(p(x,y,z),q(x,y,z),r(x,y,z))=f(x,y,z). f(p(x,y,z), q(x,y,z), r(x,y,z)) = f(x,y,z). Prove or disprove the assertion that the sequence p,q,rp,q,r consists of some permutation of ±x,±y,±z\pm x, \pm y, \pm z, where the number of minus signs is 00 or 2.2.
Putnam