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show that any positive integer is of the form 3q ,or 3q +1 or, 3q+q for some integer q

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Solution :     Let a be any positive integer and b=3 .  Applying division Lemma with a and b =3 

We have 

where   \ a= 3q+r \ 0leq r< 3 

\ Rightarrow a=3q+0 or ,     a=3q+1 or ,    a=3q+2 

\ Rightarrow a=3q     or ,    a=3q +1   or ,a=3q +2 for some integer q

 

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Deependra Verma

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