Show that square of any odd integer is of the form 4q+1.
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Answer:
We know that any positive odd integer of the form 2m +1 , 2m +3......
let a be any odd integer
then
a = 2m + 1
on squaring both sides we get
a² = (2m +1)²
a² = 4m²+4m+1
a²= 4(m²+m) + 1.
a² = 4q + 1.
( where (m²+m) = q)
proved.....
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