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x^2 + p_n * x + q_n is the square of a natural number

Source: Germany Bundeswettbewerb Mathematik 2001, Round 2, Problem 2

January 31, 2009
number theory unsolvednumber theory

Problem Statement

For each n∈N n \in \mathbb{N} we have two numbers pn,qn p_n, q_n with the following property: For exactly n n distinct integer numbers x x the number x^2 \plus{} p_n \cdot x \plus{} q_n is the square of a natural number. (Note the definition of natural numbers includes the zero here.)
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