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  • Show that any positive integer is of the form 3q or,3q+2 or 3q+2 for some integer q.

Show that any positive integer is of the form 3q or,3q+2 or 3q+2 for some integer q.

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

We have ,

\ a=3q+r

Where 

\ 0leq r< 3

⇒  a= 3q + 0  or ,a= 3q+1 or ,a=3q+2

for any integer q.

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Posted by

Deependra Verma

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