Let m > 0 be an integer, and fix z1,...,zm+1 ∈ F, w1,...,wm+1 ∈ F, where zi ̸= zj if i ̸= j. Show that there exists a unique p ∈ Pm(F) such that p(zj) = wj for j=1,...,m+1. Hint: consider the operator p→(p(z1),...,p(zm+1)).

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