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 b=2

by lemma ,a=bq+ r

a= 2q + r where r can be 0,1

let r= 0

a= 2q + 0

squaring on both side

a^2 = (2q)^2

a^2= 4q^2

let q^2 be k

hence , a^2=4k

let r=1

a=2q+l

S.O.B

a^2=(2q+1)^2

a^2= 4q^2+4q+1

= 4(q^2+q)+1

let, (q^2+q) be k

hence,a^2= 4k+1