If $m,n$ are any two odd positive integer with $n

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

Dr. Abubacker · Accepted Answer

(c)
Let $m = 2k + 1,\ n = 2k - 1\ (k \in N)$
$	herefore m^{2} - n^{2} = 4k^{2} + 1 + 4k - 4k^{2} + 4k - 1 = 8k$
Hence, All the numbers of the form $m^{2} - n^{2}$ are always divisible by 8.

Q. 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

Explanation

Reviewed by Dr. Abubacker

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