First slide

Introduction to P.M.I

Question

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

Easy

A

4
B

6
C

8
D

9

Solution

$\begin{array}{l} Let m = 2 k + 1, n = 2 k - 1 (k \in N) \\ ∴ m^{2} - n^{2} = 4 k^{2} + 1 + 4 k - 4 k^{2} + 4 k - 1 = 8 k \end{array}$
Hence, all the numbers of the form m² - n² are always divisible by 8.

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