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MATH / For a positive integer m, let f(m)=m²+m+1. Find the largest positive integer n such that 1000 f(1^2) f(2^2) dotsm f(n^2) ge f(1)^2 f(2)^2 dotsm f(n)^2.

Problem

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problem

For a positive integer m,m, let f(m)=m2+m+1f(m) = m^2 + m + 1. Find the largest positive integer nn such that \[1000 f(1^2) f(2^2) \dotsm f(n^2) \ge f(1)^2 f(2)^2 \dotsm f(n)^2.\]
Plain-text mathematical notation (without MathML)
For a positive integer m, let f(m)=m²+m+1.  Find the largest positive integer n such that
\[1000 f(1^2) f(2^2) \dotsm f(n^2) \ge f(1)^2 f(2)^2 \dotsm f(n)^2.\]
Original LaTeX notation
For a positive integer $m,$ let $f(m) = m^2 + m + 1$.  Find the largest positive integer $n$ such that
\[1000 f(1^2) f(2^2) \dotsm f(n^2) \ge f(1)^2 f(2)^2 \dotsm f(n)^2.\]

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
0cc9a4f3-0639-51f0-b46b-7dcaec69e682
task_key
intermediate~5falgebra--test--0cc9a4f3-0639-51f0-b46b-7dcaec69e682
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import