Question

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

Answer 1

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Here is your answer
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Q.Show that any positive integer is of the form 3q or ,3q+1 or , 3q+2
For some integer q

Solve:-

Let a be any positive integers and b=3.

Applying division lemma with a and ,b = 3

We have,

a = 3q + r , where 0 ≤ r < 3 and q is some integer

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

a = 3q or, a = 3q + 1 or ,a = 3q + 2 for some integers q.

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Answer 2

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Your answer is given in the attachment

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