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If n is an integer greater than 4011^2 then ...

Source: Indian National Maths Olympiad, Problem 6

February 5, 2006
inequalitiesinductioninequalities proposed

Problem Statement

(a) Prove that if nn is a integer such that n≥40112n \geq 4011^2 then there exists an integer ll such that n<l2<(1+12005)n. n < l^2 < (1 + \frac{1}{{2005}})n . (b) Find the smallest positive integer MM for which whenever an integer nn is such that n≥Mn \geq M then there exists an integer ll such that n<l2<(1+12005)n. n < l^2 < (1 + \frac{1}{{2005}})n .
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