Set theory/Listing of numbers/Polynomial law/Exercise

Find, for each of the following three sets

$\{1,3,5,7,9,\ldots \},\,\{1,2,4,8,16,\ldots \},\,\{9,99,999,9999,99999,\ldots \}$

(of the form ${}\{a_{1},a_{2},a_{3},a_{4},a_{5},\ldots \}$) a polynomial

${}P(k)=c_{0}+c_{1}k+c_{2}k^{2}+c_{3}k^{3}+c_{4}k^{4}\,$

(with coefficients ${}c_{j}\in \mathbb {Q}$) such that

$P(1)=a_{1},\,P(2)=a_{2},\,P(3)=a_{3},\,P(4)=a_{4},\,P(5)=a_{5}$

holds.

Create a solution