Question

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

Answer 1

Step-by-step explanation:

Let us take two positive integers a and b

Let b = 3

Therefore by Euclid Division Lemma

Dividend = Divisor * Quotient + Remainder

(If you don't know the above statement is also known as Euclid Disivison Lemma)

a = 3q + r

Now there are three possibilities for the value of r 0, 1 and 2.(Because if u increase above 2 then the quotient will change )

Therefore every positive integer is of the form

a = 3q

or

a= 3q +1

Or

a = 3q + 2