Question

use Euclids Division lemona to show that
the square of any
positive integer is
of the form 3p(or) 3p+1​

Answer 1

Answer:

Step-by-step explanation:

Let a be any positive integer and b=3.

Then a=3q+r for some integer q>_0 &r=0, 1,2 because 0<_r<3

Therefore a=3q or 3q +1 or 3q +2

Or a²=(3q) ² or (3q+1) ² or (3q+2) ²

a²= 9q² or 9q²+ 6q + 1 or 9 q² +12q²+4

=3×(3q²) or 3(3q²+2q) +1 or 3(3q²+4q+1) +1

=3k1 or 3k2 +1 or 3k3 +1 are some integers.

Hence it can be said that the square of any positive integer is either of the form of 3m or 3m+1.