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
Answers
Answered by
81
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
Answered by
3
Answer:
we cannot write it in any other form
Step-by-step explanation:
because there are no other possible remainders
HOPE IT HELPS
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