Question

DATE
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:

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Answer 2

Answer:

0<=r<3

possible remainders are

r=0, 1,2

if r=0

a=3q-------even number

a^2=9q^2

a^2=3×3q^2 , where m=3q^2

a^2=3m

if r=1

a=3q+1-----odd number

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

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

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

a^2=3m+1 , where m=3q^2+2q

if r=2

a^2=3m+1

Step-by-step explanation:

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