Question

use Euclid division lemma to show that the square of any positive integer is of the form of 4k,4k+1​

Answer 1

Step-by-step explanation:

let the no. = a and divisor = 2 then remainder will be 0 or 1. any one of them can possibly the remainder.

when remainder is 0

then

a= bq+r

=2q+0. ......(i)

by squaring equation (i)

(2q+0)^2

= 4q^2

=4k. where we assume q^2=k is some integer.

when remainder is 1

a=bq+r

=2q+1. ...........(ii)

by squaring equation ii

= (2q+1)^2

= 4q^2+4q+1

=4(q^2+q)+1

= 4k + 1. where we assume :q^2+q) = k

Answer 2

thank you for asking this question