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Asked by Mohit Last Modified
Answer 
The integer =z( -4,-3,-2,-1,0,1,2,3,4). Now positive integer is 1,2,3,4........the question is , X2 – X where X is a positive integer ,always divisible by 2 . If we put 1,2,3 in place of X we find 12 -1 =0 ,22 – 2 =2 , 32 -3 = 6 .so we can say “ X will be 2,3,4,5,……..(X will not be 1).”
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We prove this by mathematical induction method
If x=1 we get x2-x=0
Statement is true for x=1
Assume that statement is true for x=n, i.e., n2-n=2p for some p.
Now consider, x=n+1
(n+1)2-(n+1)=n2+1+2n-n-1=n2+n= 2p+n+n=2p+2=(2p+1)
Statement is true for x=n+1
Therefore statement is true for x is a any positive integers
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x+1=?
