Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleMedium2 minQB

MathematicsMediuminteger

If $n > 1$ is the smallest integer with the property that $n^{2} (n - 1)$ is divisible by 2009 , then the integral part of $\frac{n}{8} =$

Answer:

Solution:

Therefore, 41 must divide $n^{2} (n - 1)$ , which implies that 41 is a factor of either $n$ or $n - 1$ . In particular, $n \geq 41$ . For $n = 41$ , neither $n$ nor ( $n - 1$ ) is divisible by 7 . For $n = 42, n^{2}$ is divisible by $7^{2}$ , since n is divisible by 7 . Therefore $n = 42$ is the smallest integer.

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Fundamental Principle

⏱ 2mℹ️ Source: QB

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