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4

Part of 1985 Federal Competition For Advanced Students, P2

Problems(1)

natural numbers

Source: Austria 1985

7/7/2009
Find all natural numbers n n such that the equation: a_{n\plus{}1} x^2\minus{}2x \sqrt{a_1^2\plus{}a_2^2\plus{}...\plus{}a_{n\plus{}1}^2}\plus{}a_1\plus{}a_2\plus{}...\plus{}a_n\equal{}0 has real solutions for all real numbers a_1,a_2,...,a_{n\plus{}1}.
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