- #1
anemone
Gold Member
MHB
POTW Director
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Here is this week's POTW:
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Let $a,\, b,\, c,\, d \in \mathbb{N} $ such that the equation $x^2-(a^2+b^2+c^2+d^2+1)x+ab+bc+cd+da=0$ has an integer solution. Prove that the other solution is integer too and that both solutions are perfect squares.
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Let $a,\, b,\, c,\, d \in \mathbb{N} $ such that the equation $x^2-(a^2+b^2+c^2+d^2+1)x+ab+bc+cd+da=0$ has an integer solution. Prove that the other solution is integer too and that both solutions are perfect squares.
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