IMO 2013 Shortlist A6
Let m ‰ 0 be an integer. Find all polynomials Ppxq with real coefficients such that px3 ´ mx2 1qPpx 1q px3 mx2 1qPpx ´ 1...
Category: Algebra
Problem
Let m ‰ 0 be an integer. Find all polynomials Ppxq with real coefficients such that
px3
´ mx2
1qPpx 1q px3 mx2
1qPpx ´ 1q “ 2px3 ´ mx 1qPpxq
for all real numbers x.
(Serbia) 4 IMO 2013 Colombia