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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

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detailed solution

Correct option is C

Let m=2k+1,n=2k−1(k∈N)∴m2−n2=4k2+1+4k−4k2+4k−1=8kHence, all the numbers of the form m2 - n2 are always divisible by 8.

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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 m2−n2 is

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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