IMO 2017 Shortlist N7
Say that an ordered pair px,yq of integers is an irredu ible latti e point if x and y are relatively prime. For any nit...
Category: Number Theory
Problem
Say that an ordered pair px,yq of integers is an irredu ible latti e point if x and
y are relatively prime. For any nite set S of irredu ible latti e points, show that there is a
homogenous polynomial in two variables, fpx,yq, with integer oe ients, of degree at least 1,
su h that fpx,yq “ 1 for ea h px,yq in the set S.
Note: A homogenous polynomial of degree n is any nonzero polynomial of the form
fpx,yq “ a0xn
a1xn´1 y a2xn´2
y2
¨¨¨ an´1xyn´1
` anyn
.
(U.S.A.)