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Hi beautiful
Here is ur answer
1)
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since any +ve odd integer n is of the form 4q+1 or 4q+3
if n=4q+1
squaring both sides
n square=16q2+1+8q
8(2q2+1q)+1
8q+1 where q=2q+1
if n=4q+3
squaring both sides
n square=16q2+9+24q
8(2q2+1+3q)+1
8q+1 where q=2q2+1+3q
2)
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let 'a' be any positive integer and b=2
By euclid's division algorithm
a=bq+r 0≤r<b
a=2q+r 0≤r<2
(i.e) r =0,1
r=0 , a=2q+0=> a=2q
r=1, a=2q+1
if a is the form of 2m then 'a' is an even integer and positive odd integer is of the form 2m+1
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sapna3937:
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