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.​

Answer 1

Answer:

I think it helps you ✌️✌️

Step-by-step explanation:

Let 'a' be any positive integer and b=3

Then a=3q+r for some integer q≥0

And r=0,1,2 because 0≤r<3

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

Or,

a²=(3q)² and (3q+1)² or (3q+2)²

a²=(9q)² or 9q²+6q+1 or 9q²+12q+4

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

=3k1 or 3k2+1 or 3k3+1

Where k1=k2=k3 are some positive integers.

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

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Answer 2

Answer:

It is the correct answer.

Step-by-step explanation:

Hope this attachment helps you.