Question

Its urgent answer my question its urgent I mark as brainest

Answer 1

Answer: here bro

Step-by-step explanation:

Let us take a as any positive integer and b = 3.  

Then using Euclid’s algorithm we get a = 3q + r  here r is remainder and value of q is more than or equal to 0  and r = 0, 1, 2 because 0 < r < b  and the value of b is 3 So our possible values will 3q+0 , 3q+1 and 3q+2  

Now find the square of values  

Use the formula (a+b)² = a² + 2ab +b² to open the square bracket  

(3q)²             = 9q²   if we divide by 3 we get no remainder  

we can write it as 3*(3q²)  so it is in form of 3m  here m = 3q²  

(3q+1)²         = (3q)² + 2*3q*1  + 1²        

=9q² + 6q +1 now divide by 3 we get 1 remainder

so we can write it as 3(3q² + 2q) +1 so we can write it in form of 3m+1 and value of m is 3q² + 2q  here  

(3q+2)²         = (3q)² + 2*3q*2  + 2²  

=9q² + 12q +4  now divide by 3 we get 1 remainder  

so we can write it as 3(3q² + 4q +1) +1 so we can write it in form of 3m +1 and value of m will 3q² + 4q +1

Square of any positive integer is either of the form 3m or 3m + 1 for some integer m.