Question

use Euclid division lemma to show that the square of any positive integer is of the form 3p,3p+1.
Pls answer the question

Answer 1

Let a be any positive integer.
Euclid division lemma :-
a = bq + r
a = 3p + r (b = 3)

0 ≤ r < 3
The possible values of r are 0,1 and 2
Let the positive integers be 1,2,3,4,.....

Square of positive integer :-
1² = 1 = 3(0) + 1
2² = 4 = 3(1) + 1
3² = 9 = 3(3) + 0
4² = 16 = 3(5) + 1
5² = 25 = 3(8) + 1

Therefore, square of any positive integer is of the form 3p, 3p+1

hope it helps