Question

Prove that square of any odd integer is of the form 8p + 1 for any integer p!​

Answer 1

Answer:

According to square of any odd integer =a

a=bq+r (r=0,1,2)

b=8

a=8q+r

s.o.b.s

a²=(8q+r)²

a²= 64q²+16qr+r²

a²=8(8q²+2qr)+r²

(here 8q²+2qr=p)

a²=r²=0²=8p+0²=8p

r²=1² 8p+1²=8p+1

hence proved