Question

show that any positive integer is of the form 3m or 3m + 1 or 3m + 2 for some integer m .
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Answer 1

Answer:

Let a be a positive integer.

Then, Using Euclid's Division Lemma,

a = bq + r, 0 <= r <b, b = 3

Then, r = 0, 1, 2

If r = 0,

a = 3q+0 = 3q

If r = 1,

a = 3q + 1

If r = 2,

a = 3q + 2

In all the above cases, m = q.

Hence, any positive integer is of the form 3m, 3m + 1 or 3m + 2 for some integer m.

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