Question

4. 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 be any positive integer then it is of the form 34, 3q + or 34+2. Now square
each of these and show that they can be rewritten in the form 3mor 3m + 1.)​

Answer 1

Step-by-step explanation:

1. Let (3q)²

• so,9q²
• Take 3 as common
• so, 3(3q)²
• where 3q²=m
• so , put the value of m in 3q
• so,. 3(3q)²
• it will be 3m

2 let (3q+1)²

• so, 9q² +6q+1
• (9q²+6q) +1
• taking 3 as common so
• 3(3q²+2q)+1
• where (3q² + 2q)=m
• so ,putting the value of m
• 3(3q²+2q)+1
• 3m+1
• Hope this is helpful