Question

use equally division Lemma to show that the square of any positive integer is either of the form 3M or 3M + 1 for some integer m​

Answer 1

Answer:

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Answer 2

Answer:

Let any positive no. be a .

b=3 r=0,1,2

a=bq +r. CASE 1 a^2=(3q)^2

=9q^2

=3(3q^2) {3q^2= m}

=3m

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

=9q^2+6q+1

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

=3m+1. {3 q^2+2q=m}

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

=9q^2+12q+4

=9q^2+12q+3+1

=3(3q^2+4q+1)+1

=3m+1. {3q^2+4q+1=m}