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

Syed Pasha

Jan. 30, 2018, 7:16 p.m.

Answers!

Davneet Singh

Jan. 30, 2018, 8:10 p.m.

Hello Syed

This is directly by Euclid's Division Lemma,

If a and b are two positive integers, then

a = bq + r,

where 0 <= r < b

So,

for b = 3

a = 3q + r

where 0 <= r < 3

So, r can be 0, 1, 2

So, a = 3q, 3q + 1, 3q + 2

Where a is any positive integer

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