Question

show that the square of any positive integer is of the form 3M or 3M + 1 for some integer m​

Answer 1

Answer:

Let x be any positive integer.

Then it is of the form 3q, 3q+1,3q+2

If x=3q, then. x^2=(3q^2)=9q^2

=3.(3q^2)

=3m, where m= 3q^2

If x= 3q+1, then. x^2=(3q+1)^2

=9q^2+6q+1

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

=3m+1 where m=3q^2+2q

Thus we observed that square of any positive integer is always of the form 3m,3m+1 for some integer m.

Step-by-step explanation: