Let K {\displaystyle {}K} be a field, and let n {\displaystyle {}n} different elements a 1 , … , a n ∈ K {\displaystyle {}a_{1},\ldots ,a_{n}\in K} , and n {\displaystyle {}n} elements b 1 , … , b n ∈ K {\displaystyle {}b_{1},\ldots ,b_{n}\in K} be given.
polynomial P ∈ K [ X ] {\displaystyle {}P\in K[X]} of degree ≤ n − 1 {\displaystyle {}\leq n-1} , such that P ( a i ) = b i {\displaystyle {}P{\left(a_{i}\right)}=b_{i}}
be a
field,
and let 
different elements
,
and elements
be given.
![{\displaystyle {}P\in K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4692e3ffcbd66e900f8975113ff3f32f1cabc21a)
of degree 
, such that
