MathDB
Grade IX - Problem I

Source: Romanian National Mathematical Olympiad 2007

April 13, 2007
algebra

Problem Statement

Let a,b,c,d∈N∗a, b, c, d \in \mathbb{N^{*}} such that the equation x2−(a2+b2+c2+d2+1)x+ab+bc+cd+da=0x^{2}-(a^{2}+b^{2}+c^{2}+d^{2}+1)x+ab+bc+cd+da=0 has an integer solution. Prove that the other solution is integer too and both solutions are perfect squares.
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