If c o , c 1 , ... , C n are distinct elements of an integral

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If co, c1, ... , Cn are distinct elements of an integral domain D and do, ... , dn are any elements of D, then there is at most one polynomial ∫ of degree ≤ n in D[x] such that ∫(ci) = di for i = 0, 1, ... ,n. [For the existence of ∫, see Exercise 12].


Data from exercise 12


Lagrange's Interpolation Formula. If F is a field, a0,a1, ... , an are distinct elements of F and c0,c1, ... , Cn are any elements of F, then imageis the unique polynomial of degree ≤ n in F[x] such that ∫(ai) = Ci for all i 

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