IMO 2018 Shortlist A6
Let m,n ě 2 be integers. Let fpx1,...,xnq be a polynomial with real oe ients su h that fpx1,...,xnq “ Yx1 ... xn m ] fo...
Category: Algebra
Problem
Let m,n ě 2 be integers. Let fpx1,...,xnq be a polynomial with real oe ients
su h that
fpx1,...,xnq “
Yx1 ... xn
m
]
for every x1,...,xn P 0,1,...,m ´ 1
(
.
Prove that the total degree of f is at least n.
(Brazil)