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Grade: 10

                        

Show that n2-1 is divisible by 8, if n is an odd positive integer.

6 years ago

Answers : (2)

Pushkar Aditya
71 Points
							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 = 16m2 +8m+1 – 1= 16m2+8m = 8m(2m+1) 
n2 – 1 is divisible by 8.
When   n = 4m + 3
n2 – 1 = (4m+3) – 1 = 16m2 + 24m + 9 – 1 = 16m2 + 24m + 8 = 8(2m2 + 3m + 1)
n2 – 1 is divisible by 8.
Hence, n2 – 1 is divisible by 8 if n is an odd positive integer.
						
6 years ago
Aiman Saad Baig
39 Points
							n2 – 1 = (4m + 1)2 – 1 = 16m2 +8m+1 – 1= 16m2+8m = 8m(2m+1) 
n2 – 1 is divisible by 8.
When   n = 4m + 3
n2 – 1 = (4m+3) – 1 = 16m2 + 24m + 9 – 1 = 16m2 + 24m + 8 = 8(2m2 + 3m + 1)
n2 – 1 is divisible by 8.
Hence, n2 – 1 is divisible by 8 if n is an odd positive integer.
						
6 years ago
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