Question

use division algorithm to show that the square of any positive integer is of the form 3p or 3p+1​

Answer 1

Answer:

hope this answer helped you.

Step-by-step explanation:

To prove:Square of any positive integer is in the form 4p or 4p+1

Proof:The number may be odd or even

Case 1:If n is odd

n=2a+1

n^2=n×n

=(2a+1)(2a+1)

=4a^2+4a+1

=4(a^2+a)+1

Let a^2+a be p

n^2=4p+1

Case 2:If n is even

n=2a

n^2=2a×2a

n^2=4a^2

Let a^2 be p

n^2=4p

Hence proved.

Answer 2

Answer:

step

Step-by-step explanation:

step 1 - we know that a = bq + r

let a be the square of the integer and b be any positive integer

then, a= ( 3) 2

= 9

again a= (3p+ 1) 2

we know that ( a+ b) 2= a2 + b2 + 2ab

9p2 + 1 + 6p

and so on