MathDB

Let

n\ge 2

be an integer. We call an ordered

n

-tuple of integers primitive if the greatest common divisor of its components is

1

. Prove that for every finite set

H

of primitive

n

-tuples, there exists a non-constant homogenous polynomial

f(x_1,x_2,\ldots,x_n)

with integer coefficients whose value is

1

at every

n

-tuple in

H

.
Based on the sixth problem of the 58th IMO, Brazil

A. 703