A divided-difference characterization of polynomials over a general field

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) It is proved that, for an arbitrary field K not of characteristic 2 and arbitrary ..., if functions f : K[arrow right]K and h : K[arrow right]K satisfy f [x^sub 1^, . . . , x^sub n^] = h (x^sub 1^ + . . . + x^sub n^) whenever x^sub 1^, . . . , x^sub n^ are distinct elements of K, then f is equal to a polynomial of degree at most n over K. (Here f [x^sub 1^, . . . , x^sub n^] denotes the divided difference of f at the distinct points x^sub 1^, . . . , x^sub n^.) The case of a field of characteristic 2 is also considered. [PUBLICATION ABSTRACT]