Question

m²- 1 is divisible by 8. If mis
(a) an even integer (b) an odd
integer (c) a natural number ()
a whole number​

Answer 1

Answer:

Let a = n2 - 1

Here n can be ever or odd.

Case I n = Even i.e., n = 2k, where k is an integer.

⇒ a = (2k)2-1

⇒ a = 4k2 - 1

At k = -1, = 4(-1)2 - 1 = 4 - 1 = 3, which is not divisible by 8.

At k = 0, a = 4(0)2 - 1 = 0 - 1 = -1,which is not divisible by 8 , which is not

Case II n = Odd i.e., n = 2k + 1, where is an odd integer .

⇒ a = 2k + 1

⇒ a = (2k+1)2 - 1

⇒ a = 4k2 + 4k + 1 - 1

⇒ a = 4k2 + 4k

⇒ a = 4k(k+1)

At k = -1, a = 4(-1)(-1+1) = 0 which is divisible by 8.

At k = 0, a = 4(0)(0+1) = 4 which is divisible by 8 .

At k = 1, a = 4(1)(1+) = 8 which is divisible by 8.

Hence , we conclude from above two cases , if n is odd, then n2 - 1 is      

  your question is wrong in the place of m^2 I am written n^2ok

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