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Generalisation of IMO 2017 P6

Source: KoMaL A. 703

May 21, 2023
number theory

Problem Statement

Let n≥2n\ge 2 be an integer. We call an ordered nn-tuple of integers primitive if the greatest common divisor of its components is 11. Prove that for every finite set HH of primitive nn-tuples, there exists a non-constant homogenous polynomial f(x1,x2,…,xn)f(x_1,x_2,\ldots,x_n) with integer coefficients whose value is 11 at every nn-tuple in HH.
Based on the sixth problem of the 58th IMO, Brazil
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