show that square of an odd positive
Integer is of the form 8q+1, for
some positive integer q.
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Answer:
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
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