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A4

Part of 1987 Putnam

Problems(1)

Putnam 1987 A4

Source:

8/5/2019
Let PP be a polynomial, with real coefficients, in three variables and FF be a function of two variables such that P(ux, uy, uz) = u^2 F(y-x,z-x)   \mbox{for all real $x,y,z,u$}, and such that P(1,0,0)=4P(1,0,0)=4, P(0,1,0)=5P(0,1,0)=5, and P(0,0,1)=6P(0,0,1)=6. Also let A,B,CA,B,C be complex numbers with P(A,B,C)=0P(A,B,C)=0 and ∣B−A∣=10|B-A|=10. Find ∣C−A∣|C-A|.
Putnam