Um da Putnam...
ai and bi are constants. Let A be the (n+1) x (n+1) matrix Aij, defined as follows: Ai1 = 1; A1j = xj-1 for j ≤ n; A1 (n+1) = p(x); Aij = ai-1j-1 for i > 1, j ≤ n; Ai (n+1) = bi-1 for i > 1. We use the identity det A = 0 to define the polynomial p(x). Now given any polynomial f(x), replace bi by f(bi) and p(x) by q(x), so that det A = 0 now defines a polynomial q(x). Prove that f( p(x) ) is a multiple of ∏ (x - ai) plus q(x). ===== TRANSIRE SVVM PECTVS MVNDOQVE POTIRI CONGREGATI EX TOTO ORBE MATHEMATICI OB SCRIPTA INSIGNIA TRIBVERE Fields Medal(John Charles Fields) ______________________________________________________________________ Yahoo! Mail - O melhor e-mail do Brasil! Abra sua conta agora: http://br.yahoo.com/info/mail.html ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~nicolau/olimp/obm-l.html =========================================================================