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Geometric Progression

If m, n are...

Question

If $m, n$ are any two odd positive integers and $n < m$ , then the largest positive integer which divides all the numbers of the type $m^{2} - n^{2}$ is

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Solution

The correct option is C $8$
Take, $n = 2 k - 5, m = 2 k - 1$

$∴ m^{2} - n^{2}$ $= (m + n) (m - n)$

$= (4 k - 6) (4)$

$= 8 (2 k - 3)$ , which is divisible by $8.$

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