show that square of any positive integer is of form 3q or 3q+1 for some integers q
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a=bq+r
b=3. r=0;1;2
when r =0
a=3q
a^2=9q^2
a^2=3(3q)=3q
when r=1
a=3q+1
a^2=(3q+1)^2
=(9q^2+6q+1)
=3(3q+2)+1
=3q+1
b=3. r=0;1;2
when r =0
a=3q
a^2=9q^2
a^2=3(3q)=3q
when r=1
a=3q+1
a^2=(3q+1)^2
=(9q^2+6q+1)
=3(3q+2)+1
=3q+1
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