if 'n' is an integer,then show that
is divisible by 8
MitheshShankar:
Show that n2-1 is divisible by 8, if n is an odd positive integer.
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Answered by
1
put the value of n 1
then we get 8*1 = 8
put the value of n 2
then we get 8*4= 32
put the value of n 3
then we get 8*9 = 72
So n2 is divisible by 8
Hope It will help you
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then we get 8*1 = 8
put the value of n 2
then we get 8*4= 32
put the value of n 3
then we get 8*9 = 72
So n2 is divisible by 8
Hope It will help you
please Mark me as brainlest
Answered by
1
for the question "Show that n2-1 is divisible by 8, if n is an odd positive integer."
here is the solution
Any odd positive integer is of the form
4m + 1 or 4m + 3 for some integer m.
When n = 4m + 1,
n2 – 1 = (4m + 1)2 – 1
= 16 +8m+1 – 1
= 16+8m
= 8m(2m+1) – 1 is divisible by 8. When n = 4m + 3 – 1
= (4m+3) – 1 = 16 + 24m + 9 – 1
= 16 + 24m + 8 = 8(2 + 3m + 1) – 1 is divisible by 8.
Hence, – 1 is divisible by 8 if n is an odd positive integer.
here is the solution
Any odd positive integer is of the form
4m + 1 or 4m + 3 for some integer m.
When n = 4m + 1,
n2 – 1 = (4m + 1)2 – 1
= 16 +8m+1 – 1
= 16+8m
= 8m(2m+1) – 1 is divisible by 8. When n = 4m + 3 – 1
= (4m+3) – 1 = 16 + 24m + 9 – 1
= 16 + 24m + 8 = 8(2 + 3m + 1) – 1 is divisible by 8.
Hence, – 1 is divisible by 8 if n is an odd positive integer.
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