MathDB

Let

F(x,y)

and

G(x,y)

be relatively prime homogeneous polynomials of degree at least one having integer coefficients. Prove that there exists a number

c

depending only on the degrees and the maximum of the absolute values of the coefficients of

F

and

G

such that

F(x,y)\neq G(x,y)

for any integers

x

and

y

that are relatively prime and satisfy

\max \{ |x|,|y|\} > c

. [K. Gyory]

Problem Statement