MathDB
polynomials

Source: Vietnam TST 2008, Problem 2

September 5, 2008
algebrapolynomialalgebra proposed

Problem Statement

Find all values of the positive integer m m such that there exists polynomials P(x),Q(x),R(x,y) P(x),Q(x),R(x,y) with real coefficient satisfying the condition: For every real numbers a,b a,b which satisfying amāˆ’b2=0 a^m-b^2=0, we always have that P(R(a,b))=a P(R(a,b))=a and Q(R(a,b))=b Q(R(a,b))=b.
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