Question

Use Euclid division lemma to show the square of any possitive integer is either of the form 3m or 3m+1 for some integer m

Answer 1

a =bq+r

a is any positive integer

possible remainder = 0,1,2

For r=0

a = 3q+0

a^2= 3q^2

a^2=9q^2 (3×3q^2

a= 3m (where 3q^2=m

For r=1

a= 3q+1

a^2= (3m+1)^2

a^2= 9q^2+6q+1

a^2=3(3q^2+2q)+1

a = 3m+1(3q^2+2q = m

Answer 2

Answer:

It is the correct answer.

Step-by-step explanation:

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