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Omni-MATH / Let P(x) be the monic polynomial with rational coefficients of minimal degree such that (1)/(√(2)), (1)/(√(3)),(1)/(√(4)),…,(1)/(√(1000)) are roots of P. What is the sum of the coe…

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problem

Let P(x)P(x) be the monic polynomial with rational coefficients of minimal degree such that 12\frac{1}{\sqrt{2}}, 13,14,…,11000\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{4}}, \ldots, \frac{1}{\sqrt{1000}} are roots of PP. What is the sum of the coefficients of PP?
Plain-text mathematical notation (without MathML)
Let P(x) be the monic polynomial with rational coefficients of minimal degree such that (1)/(√(2)), (1)/(√(3)),(1)/(√(4)),…,(1)/(√(1000)) are roots of P. What is the sum of the coefficients of P?
Original LaTeX notation
Let $P(x)$ be the monic polynomial with rational coefficients of minimal degree such that $\frac{1}{\sqrt{2}}$, $\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{4}}, \ldots, \frac{1}{\sqrt{1000}}$ are roots of $P$. What is the sum of the coefficients of $P$?

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task_id
e1946876-90e9-59dd-9a5c-9a2adb652979
task_key
test--e1946876-90e9-59dd-9a5c-9a2adb652979
task_revision_id
1
config / split
/ test

Official source

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