Question

use euclid's division Lemma to show that the square of any positive integer is either of the form 3M or 3M + 1 for some integer m. [Hint: let x beany possitive integer then it is of the form 3q,3q+1,3q+2,. now square each of these and show that they can be rewritten in tje form 3m or 3m+1.].​

Answer 1

we know that Euclid division lemma is

a=bq+r

Answer 2

Answer:

let x be any positive integer and b=3;then

by euclid's division lemma

x=bq+r

then positive integers are of the form

3q,3q+1,3q+2