Question

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

Answer 1

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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