Question

a positive integer is of form 3q+1 , q being a natural number . can you write its square in any form other than 3m+1, i.e, 3m or 3m+2 for some integer m justify your answer​

Answer 1

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Note: the numbers after variables are their powers.

It is necessary to solve all the values of r in the exam

Answer:

By using Euclid's Division Lemma, a=bq+r

Where, 0 ≤ r < b here, b=3 therefore, r= 0,1 or 2

So,

1. r= 0

2. r= 1

(skipping to r= 2 NOT TO BE DONE IN EXAM)

3. r= 2

a²= (3q+2)²

a²= 9q² + 12q + 4

a²= 3(3q² + 4q) + 4

Now, let (3q2 + 4q) be m

Therefore, a²= 3m + 4

Answer 2

Answer:

we cannot write it in any other form

Step-by-step explanation:

because there are no other possible remainders

HOPE IT HELPS