Question

show that square of any positive odd integer is of the form of 8q+1.

Answer 1

a = bq + r

a = 8q + r

0 ≤ r < 8

The possible values of r are 0,1,2,3,4,5,6, and 7

Let a be any positive odd integer,

a = {1,3,5,7....}

Square of any positive odd integer

1² = 1 = 8(0)+1

3² = 9 = 8(1)+1

5² = 25 = 8(3)+1

7² = 49 = 8(6)+1

Therefore,square of any positive odd integer is of the form 8q+1

Hence proved.

Hope it helps