Question

Show that any positive no is in the form of 3q, 3q+1 and 3q+2

Answer 1

y is any integer

y=3q

y^2=9q^2

y^2=3(3q^2)

y^2=3q, 3q^2=q

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y=3q+1

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

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

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

y^2=(3q+1)

3q^2+2q=q

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y=3q+2

y^2=(3q+2)^2

y^2=9q^2+12q+4

y^2=3(3q^2+4q+1)+1

y^2=(3q+1) [3q^2+4q+1 be q]

it is showing that q^2 is in 3q and 3(q+1) but not in 3(q+2)