Question

Show that the square of any +ve odd integer is of the form 8m+1 for some integer m

Answer 1

let x be the positive integer
x=8m+1
x²=(8m+1)²
x²=(8m)²+2*8m*(1)+1
x²=64m²+16m+1
x²=8(8m²+2m)+1
x²=8m+1 [ let 8m²+2m =m]
∴ proved