Question

use Euclids division lemma to show that the square of any positive integer is of the form 3p,3p+1. please solve the problem very urgent ​

Answer 1

Step-by-step explanation:

your question is done by this method only from the place of q replace p

you try to di this question

And not forget to make as me BRAINLIST

Answer 2

Answer:

Step-by-step explanation:

Let a be the positive integer and b=3.

We know a=bq+r, 0≤r<b

Now, a=3q+r, 0≤r<3

The possibilities of remainder is 0,1, or 2.

Case 1 : When a=3q

(a)^2  = (3q)^2

        =9q^2

=3q×3q=3m where m=3q ^2

Case 2 : When a=3q+1

(a)^2 =(3q+1)^2

        =(3q)^2+(2×3q×1)+(1)^2

=3q(3q+2)+1=3m+1 where m=q(3q+2)

Case 3: When a=3q+2

(a)^2 =(3q+2)^2

=(3q)^2 +(2×3q×2)+(2) ^2

 =(9q)^2 +12q+4

=9q^2+12q+3+1=3(3q^2) +4q+1)+1=3m+1  

where m=(3q)2 +4q+1

Hence, from all the above cases, it is clear that square of any positive integer is of the form 3m or 3m+1.