zeracuse

Posted on February 3, 2014

(inspired from a good Russian algebra problem)

sometimes you just think too much …

PROBLEM

Let $P(x)$ and $Q(x)$ be (monic) polynomials with real coefficients (the first coefficient being equal to $1$ ), and $deg(P(x)) = deg(Q(x))=10$ . Prove that if the equation $P(x) = Q(x)$ has no real solutions, then $P(x+1)=Q(x-1)$ has a real solution.