1.

Show that any positive integer is of the form 3q or 3q+1 or 3q+2 for some integer q.

Answer» Let any positive integer be q. If divide q by 3 we get the remainders 0,1,2 which can be written as 3q, 3q+1, 3q+2 for some integer q. Hence any positive integer is of the form 3q or 3q+1 or 3q+2.
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