IMO 2015 Shortlist A6
Let n be a fixed integer with n ě 2. We say that two polynomials P and Q with real coefficients are block-similar if for...
Category: Algebra
Problem
Let n be a fixed integer with n ě 2. We say that two polynomials P and Q with real coefficients are block-similar if for each i P t1,2,...,nu the sequences Pp2015iq,Pp2015i´ 1q,...,Pp2015i ´ 2014q and Qp2015iq,Qp2015i´ 1q,...,Qp2015i ´ 2014q are permutations of each other. paq Prove that there exist distinct block-similar polynomials of degree n ` 1. pbq Prove that there do not exist distinct block-similar polynomials of degree n. (Canada) 4 IMO 2015 Thailand