Show that n^2-1 is divisible by 8,if 'n' is an odd positive integer.

Answers (1)

Any odd positive integer is of the form 4m+1 or 4m+3 for some integer m
for n = 4m+1 
n^2-1 = (4m+1)^2 - 1
        = 16m^2 + 8m
        = 8(2m^2 + m)
hence it is divisible by 8
for n = 4m+3
 n^2 - 1 = 16m^2 + 24m + 8
          = 8(2m^2 + 3m + 1)
it is also divisible by 8

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