Question

used Etios division Lemma to show that the square of any positive integer is either of in the form 3M or 3M + 1 for some integer m

Answer 1

Firstly,it is Euclid's division lemma.

Now to the solution,

Let a be any positive integer and b=3.

Every positive integer is of the form 3q or 3q+1

This arises two cases over here;

CASE 1: When a = 3q

a^2=(3q)^2
=3q(3q)
3m,where m=q(3q)


CASE 2: When a = 3q +1

a^2=(3q+1)^2
=9q^2+6q+1
=3q(3q+2)+1
3m+1,where m=3q(3q+2)


I hope it helps you!!!!!

Answer 2

Answer:

It is the correct answer.

Step-by-step explanation:

Hope this attachment helps you.